A “good confession,” as a phrase, has been pinched by the Catholics and any Internet search will teach you how to make a good confession in the confessional and thereafter make penance etc. But in this case, Paul is referring to a “confession of faith” which has been appropriated by yet another clerics to represent a formal statement of beliefs by one denomination for another. They are crafted documents and in most cases, cover a wide range of potential controversies discussed by believers through the centuries. But honestly, the confessions of Timothy and the Christ were much more personal. They simply acknowledged who they each were and to whom they belonged and gave fealty.
Fight the good fight of the faith. Take hold of the eternal life to which you were called when you [Paul to Timothy] made your good confession in the presence of many witnesses. . . . I command you in the presence of God, who gives life to all things, and Christ Jesus, who made the good confession [Paul about Jesus] when testifying before Pontius Pilate. [I Timothy 6:12-13, CEB]
There are people who get all “hinky” about the term, saved, as in “Are you saved?” But I think it’s really just a shortcut question about one’s confession. They are asking, “do you profess the Christ?” Do you follow the One God? Do you believe that Jesus was God in the flesh during a particular period of history and yet died and resurrected into a different kind of “body” and heretofore communes intimately with the God of the Universe to this day? Or, even this, do you believe in the Presence and transforming power of a Holy Spirit who lives within, upon invitation, and opens a Way to heaven on earth in preparation for eternity?
What do you believe? What is real to you? Who is this Jesus to you? Whom do you confess?
“This is also why I’m suffering the way I do, but I’m not ashamed. I know the one in whom I’ve placed my trust. I’m convinced that God is powerful enough to protect what he has placed in my trust until that day.” [II Timothy 1:12, CEB]
Meditations from Zion 
I believe the word you should be using is “a profession” of faith. NOT “confession”. I think you have the terms confused.
Actually, there are documents such as the Westminster Confession of Faith and more. A quick Google search will confirm my use of this term. But thanks for reading. ☺