It is to be noted what kind of elders are to be especially honoured and rewarded. It is those who toil in preaching and teaching. The elder whose service consisted only in words and discussion and argument is not in question here. Those whom the Church really honoured were the ones who worked to edify and build it up by preaching the truth and by educating the young and the new converts in the Christian way.

(2) It was Jewish law that no one should be condemned on the evidence of a single witness: ‘A single witness shall not suffice to convict a person of any crime or wrongdoing in connection with any offence that may be committed. Only on the evidence of two or three witnesses shall a charge be sustained’ (Deuteronomy 19:15). The Mishnah, the codified Rabbinic law, in describing the process of trial, says: ‘The second witness was likewise brought in and examined. If the testimony of the two was found to agree, the case for the defence was opened.’ If a charge was supported by the evidence of only one witness, it was held that there was no case to answer.

Quoted verse:
Deuteronomy 19:15 but I will read verses 15 through 21.  These scriptures are linked clearly to the instructions in Matthew 18 or the "offending brother resolution instructions."  The God-given concepts are equal.

Deuteronomy 19:15-21
15 One witness shall not rise up against a man for any iniquity, or for any sin, in any sin that he sinneth: at the mouth of two witnesses, or at the mouth of three witnesses, shall the matter be established.
16 If a false witness rise up against any man to testify against him that which is wrong;
17 Then both the men, between whom the controversy is, shall stand before the LORD, before the priests and the judges, which shall be in those days;
18 And the judges shall make diligent inquisition: and, behold, if the witness be a false witness, and hath testified falsely against his brother;
19 Then shall ye do unto him, as he had thought to have done unto his brother: so shalt thou put the evil away from among you.
20 And those which remain shall hear, and fear, and shall henceforth commit no more any such evil among you.
21 And thine eye shall not pity; but life shall go for life, eye for eye, tooth for tooth, hand for hand, foot for foot.

In later times, church regulations laid it down that the two witnesses must be Christian [Spirit-holding firstfruits], for it would have been easy for a malicious non-Christian to make up a false charge against a Christian elder in order to discredit him, and through him to discredit the Church. In the early days, the Church authorities did not hesitate to apply discipline; and Theodore of Mopseuestia, one of the early fathers who lived in the late fourth and early fifth centuries, points out how necessary this regulation was, because the elders were always liable to be disliked and were especially open to malicious attack ‘due to the retaliation by some who had been rebuked by them for sin’. Those who had been disciplined might well seek to get their own back by maliciously charging an elder with some irregularity or some sin.

The fact remains that this would be a happier world – and the Church, too, would be happier – if people would realize that it is nothing less than sin to spread stories of whose truth they are not sure. Irresponsible, slanderous and malicious talk does infinite damage and causes infinite heartbreak, and such talk will not go unpunished by God.

(3) Those who persist in sin are to be publicly rebuked [meaning within the congregation of firstfruits]. That public rebuke had a double value. It sobered sinners into a consideration of their ways, and it made others take care that they did not involve themselves in a similar humiliation. The threat of publicity is no bad thing if it keeps people on the right path, even through fear. A wise leader will know the time to keep things quiet and the time for public rebuke. But, whatever happens, the Church must never give the impression that it is condoning sin.

(4) Timothy is urged to administer his office without favoritism or prejudice. The biblical scholar B. S. Easton writes: ‘The well-being of every community depends on impartial discipline.’ Nothing does more harm than when some people are treated as if they could do no wrong and others as if they could do no right. Justice is a universal virtue, and the Church must surely never fall below the impartial standards which even the world demands.

(5) Timothy is warned not to be too hasty ‘in laying hands on any man’. That may mean one of two things.

(a) It may mean that he is not to be too quick in laying hands on any man to ordain him to office in the Church. Before people gain promotion in business, or in teaching, or in the army or the navy or the air force, they must prove that they deserve it. No one should ever start at the top. This is doubly important in the Church, for those who are raised to high office and then fail in it bring dishonour, not only on themselves, but also on the Church. In a critical world, the Church cannot be too careful in regard to the kind of men and women whom it chooses as its leaders.

(b) In the early Church, it was the custom to lay hands on a sinner who repented, who had given proof of repentance and who had returned to the fold of the Church. It is laid down: ‘As each sinner repents, and shows the fruits of repentance, lay hands on him, while all pray for him.’ The early Church historian Eusebius tells us that it was the ancient custom that repentant sinners should be received back with the laying on of hands and with prayer. If that is the meaning here, it will be a warning to Timothy not to be too quick to receive back anyone who has brought disgrace on the Church, to wait until the individual has shown genuine [repentance and invoking of Godly principles-fruit] and a true determination to live according to that declaration of repentance. That is not for a moment to say that such a person is to be held at arm’s length and treated with suspicion, but rather to be treated with all sympathy and with all help and guidance in the period of probation. But it is to say that membership of the Church is never to be treated lightly, and that people must show their [repentance] for the past and their determination for the future before they are received not into the fellowship of the Church but into its membership. The fellowship of the Church exists to help such people redeem themselves, but its membership is for those who have truly pledged their lives to Christ. ~Barclay Commentary

Now to the commentaries.

Looking at the commentaries, they generally divide this long verse into six parts:

1] I charge thee before God.
2] And the Lord Jesus Christ
3] And the elect angels.
4] That thou observe these things.
5] Without preferring one before another.
6] Doing nothing by partiality.

1] I charge thee before God.
I charge thee — rather as Greek, “I adjure thee”; so it ought to be translated. ~Jamieson, Fausset, Brown

Before God - Before: in the presence of God. God: omitted in the oldest manuscripts God the Father, and Christ the Son, will testify against thee, if thou disregardest my injunction. He vividly sets before Timothy the last judgment, in which God shall be revealed, and Christ seen face to face with His angels ~Jamieson, Fausset, Brown

I charge thee before God - The word rendered “charge” means, properly, to call to witness; then to affirm with solemn attestations; and then to admonish solemnly, to urge upon earnestly. It is a word which implies that the subject is of great importance. Paul gives this charge as in the presence of God, of the Redeemer, and of the elect angels, and wishes to secure that sense of its solemnity which must arise from the presence of such holy witnesses. ~Barnes Notes

I charge thee before God - The apostle would have Timothy to consider that all he did should be done as in the sight of God, the Father of the spirits of all flesh; in the sight of Christ, the Savior of sinners, who purchased the Church with his own blood; and in the sight of the most holy, approved, and eminent angels, whose office it was to minister to the heirs of salvation. The word εκλεκτοι, elect, applied to the angels here, is supposed to distinguish those who stood, when others fell from their first estate. The former were elect, or approved; the latter reprobate, or disapproved. This is not an unfrequent sense of the word εκλεκτος, elect. Perhaps there is nothing else meant than the angels that are chosen out from among others, by the Lord himself, to be ministering servants to the Church. ~Adam Clarke

I charge thee before God - Who sees and knows all things, and is a righteous and most impartial Judge; with whom there is no respect of persons, and in whose place and stead, the judges of the earth, both civil and ecclesiastical, stand; and to whom they are accountable for the judgment they pass on men and things; and in whose house or church Timothy was, whose business he was doing, and which ought to be done, with a view to his glory; wherefore the apostle gives him this solemn charge as in his sight: ~John Gill

2] And the Lord Jesus Christ
And the Lord Jesus Christ - As in the presence of the Lord Jesus; with his eye resting upon you. ~Barnes Notes

And the Lord Jesus Christ - who also is God omniscient; and is Jesus Christ the righteous, the Head of the church, and the Judge of quick and dead; before whose judgment seat all must appear; where there will be no respect of persons, nor any partiality used. ~John Gill

3] And the elect angels.
And the elect angels - It is not uncommon in the Scriptures to speak as if we were in the presence of holy angels. No one can prove that the angels are not witnesses of what we do. Sin, too, should be avoided as if every eye in the universe were upon us. How many things do we do which we would not; how many feelings do we cherish which we would at once banish from our minds, if we felt that the heavens above us were as transparent as glass, and that all the holy beings around the throne were fixing an intense gaze upon us! The word “elect” here seems to imply that there had been some influence used to keep them, and some purpose respecting them, which had not existed in regard to those who had fallen. Saints are called “elect” because they are chosen of God unto salvation, and it would appear that it is a great law extending through the universe, that both those who remain in a state of holiness, and those who are made holy, are the subjects of purpose and choice on the part of God. ~Barnes Notes

The elect angels - Why "elect" we do not certainly know. They may be the good angels as distinct from the bad angels, or those who were chosen to assist in the work of human redemption may be meant. Angels are often mentioned in this connection. ~People's New Testament

4] That thou observe these things.
That thou observe these things - Probably referring to all the things which he had enjoined in the previous parts of the Epistle. ~Barnes Notes

That thou observe these things - either all that are contained in the epistle, or more particularly the rules prescribed in this chapter; concerning rebuking members of a different age and sex, providing for poor widows, and taking care of the ministers of the Gospel, and chiefly what regards the discipline of the church with respect to the elders of it; as not to admit an accusation against them, unless it is sufficiently evident, and yet not connive [scheme, plot, or cooperate secretly in an illegal or wrongful action] at notorious sinners, but rebuke them publicly; and this charge belongs not only to Timothy, but to the whole church, and to all succeeding ministers and churches in all ages. ~John Gill

5] Without preferring one before another.
Without preferring one before another — rather as Greek, “prejudice”; “judging before” hearing all the facts of a case. There ought to be judgment, but not prejudging. ~Jamieson, Fausset, Brown

Without preferring one before another - Margin, “prejudice.” The meaning is, “without previous judgment” - without any prejudice on account of rank, wealth, personal friendship, or predilection of any sort. Let there be entire impartiality in all cases. Justice was beautifully represented by the ancients as holding a pair of scales equally balanced. It is as important that there should be entire impartiality in the church as in civil transactions, and though it is not wrong for a minister of the gospel to have his personal friends, yet in the administration of the affairs of the church he should remember that all are brethren, and all, of whatever rank, color, sex, or age, have equal rights. ~Barnes Notes

Without preferring one before another - Χωρις προκριματος· Without prejudice. Promote no man’s cause; make not up thy mind on any case, till thou hast weighed both sides, and heard both parties, with their respective witnesses; and then act impartially, as the matter may appear to be proved. Do not treat any man, in religious matters, according to the rank he holds in life, or according to any personal attachment thou mayest have for him. Every man should be dealt with in the Church as he will be dealt with at the judgment-seat of Christ. A minister of the Gospel, who, in the exercise of discipline in the Church, is swayed and warped by secular considerations, will be a curse rather than a blessing to the people of God. Accepting the persons of the rich, in ecclesiastical matters, has been a source of corruption in Christianity. With some ministers the show of piety in a rich man goes farther than the soundest Christian experience in the poor. What account can such persons give of their stewardship? ~Adam Clarke

Without preferring one before another - or, as the words may be rendered, "without prejudgment"; that is, without prejudging a case, or determining, before hearing, how it shall be; or as the Syriac version renders it, "in nothing let thy mind be prepossessed"; the sense is, that he should attend to any case that should come before him in the church, without prejudice or prepossession, and hearken to what is said on both sides; and judge impartially, and not in haste, but weigh well and consider the evidence that is given, and then determine as the case appears; so the Arabic version renders it, "without haste", or precipitancy [pre·cip·i·tance-cy] [rash haste]; to which agrees the advice of the men of the great congregation, or Ezra's congregation, who were in his time, and succeeded him; הוו מתונים בדין, "be slow in judgment" (k), or long at it; that so by strict and close examination, things not known at first may be discovered: and when judgment is passed, it should not be through affection to one party, and disrespect to another; which is called in Scripture a respect of persons, and here a preferring one to another; and which is further explained by adding, [doing nothing by partiality]. ~John Gill

6] Doing nothing by partiality.
Doing nothing by partiality - Greek, “inclination,” or “proclivity” - that is, without being inclined to favor one party or person more than another. There should be no purpose to find one guilty and another innocent; no inclination of heart toward one which would lead us to resolve to find him innocent; and no aversion from another which would make us resolve to find him guilty. ~Barnes Notes

Doing nothing by partiality - or by inclining to one side more than to another. A judge should not preponderate to either side, but should hold the balance of justice even, and do nothing to turn the scale one way or another, but as the weight and truth of the evidence direct; and such a rule should be observed in all church affairs. ~John Gill