"Remember your leaders, those who spoke to you the word of God. Consider the outcome of their way of life, and imitate their faith." - Hebrews 13:7 ESV
The word translated 'imitate' here is Mimeomai (Strong's G3401). It is the same word that mime comes from.
It is the same word used here...
"Now we command you, brothers, in the name of our Lord Jesus Christ, that you keep away from any brother who is walking in idleness and not in accord with the tradition that you received from us. For you yourselves know how you ought to imitate us, because we were not idle when we were with you, nor did we eat anyone's bread without paying for it, but with toil and labor we worked night and day, that we might not be a burden to any of you. It was not because we do not have that right, but to give you in ourselves an example to imitate." - 2 Thessalonians 3:6-9 ESV
Really the faith we have, if we have it, is the faith of the Son of God. Many modern translations turn this into 'faith in the Son of God' but the Greek is very clear.
The faith we follow when we follow another person's faith is the faith of Jesus Himself. At first we don't realize that. We can't realize it. We give glory to people even if they deflect it because we see their faith as a personal ability that they possess.
If they are truly walking by faith then they know their faith is a gift.
When, if ever, do we stop miming the faith of other people?
"I am crucified with Christ: nevertheless I live; yet not I, but Christ liveth in me: and the life which I now live in the flesh I live by the faith of the Son of God, who loved me, and gave himself for me." - Galatians 2:20 KJV
Paul never indicated that those who heard him should ever stop. Even this verse about being crucified with Christ that we sing about was written by Paul explaining His process that he encouraged everyone who heard him to adopt.
"Just as Jannes and Jambres opposed Moses, so these men also oppose the truth, men corrupted in mind and disqualified regarding the faith. But they will not get very far, for their folly will be plain to all, as was that of those two men. You, however, have followed my teaching, my conduct, my aim in life, my faith, my patience, my love, my steadfastness, my persecutions and sufferings that happened to me at Antioch, at Iconium, and at Lystra -- which persecutions I endured; yet from them all the Lord rescued me." - 2 Timothy 3:8-11 ESV
Paul takes ownership of Christ's faith and makes the comparison to Moses and Pharaoh's sorcerers who opposed God's work by opposing God's man.
"Obey them that have the rule over you, and submit yourselves: for they watch for your souls, as they that must give account, that they may do it with joy, and not with grief: for that is unprofitable for you." - Hebrews 13:17 KJV
Who has rule over us? The person who we submit to that's who. Not a person who just by circumstances is telling us what to do. That authority is illegitimate unless it is given by God.
There is point in time when we see a person, and it isn't often, who loves God and who cares for our soul. That person is walking by faith. That person personalizes their faith walk and lives crucified with Christ and loves by faith. That person is a teacher, though the may or may not have the gift of teaching, and a shepherd who feeds Jesus' sheep.
There is moment when we realize, 'That is my person. They are a gift from God for my life. I want to be the person I will become if I am associated with that person. They help me grow and will help me grow.' or even in some cases, 'That is my Pastor.' In those cases we come under the vision that God has given to those men. There will be places where we fit right in and have an important role in the success of the enterprise.
If God invests that kind of love in a person for us they will one day stand before Him and give an account of that stewardship. We may never have submitted to their leadership, such as it was, but still they will give an account and their account will be a direct reflection on our lives when it is time to hand out the rewards in the future.
God tells us to pray for those people whose faith we follow. It is a very good idea since our outcome is tied to their outcome in a real way.
I want to follow the faith of those that love Jesus and love me for the rest of my life and for the rest of theirs. I want to live with a sense of accountability to certain grace men and have a sense of lifelong loyalty even if God's plan has brings us in different directions. I want to watch closely (or from afar) where their faith brings them in this life and then trust in where they have gone after their eventual earthly death.
Grace men won't Lord over you in an intrusive way and if they are intrusive at times you can tell them and in humility they will back off or press forward as they see fit.
When do we stop following and honoring? Never. We just find the God who they follow, make Him our own and have a faith worthy of following that has no middle man. We grow and stop attributing what is coming from a man to the man. We honor God as God and men as men of God.
This is not a popular doctrine these days. I imagine it never has been. Fortunately my interest is not in being popular but it is in having the mind of Christ.