Incidental evidence is a particularly strong form of support, because there is no obvious reason to fabricate. In Acts and in First Peter we have Peter contrasting silver and and gold with the things of God. I cannot think of another recorded instance of the contrast existing as to the other NT figures. Moreover the small amount of actual words from Peter makes the phrase more striking.
I am not aware of anyone who contends Acts and First Peter written by the same person or in some sort of scheme to create a consistent figure of Peter. Therefore, the easiest inference is that both writings go back to the same person. Indeed if it were not for the other claims of Christianity (if these were merely other ancient documents) then such a connection would probably not even be an issue.
Here is the section from First Peter 1:
17 And if you call on him as Father who judges impartially according to each one’s deeds, conduct yourselves with fear throughout the time of your exile,
18 knowing that you were ransomed from the futile ways inherited from your forefathers, not with perishable things such as silver or gold,
19 but with the precious blood of Christ, like that of a lamb without blemish or spot.
20 He was foreknown before the foundation of the world but was made manifest in the last times for the sake of you
21 who through him are believers in God, who raised him from the dead and gave him glory, so that your faith and hope are in God.
Here is Peter in Acts 3:
1 Now Peter and John were going up to the temple at the hour of prayer, the ninth hour.
2 And a man lame from birth was being carried, whom they laid daily at the gate of the temple that is called the Beautiful Gate to ask alms of those entering the temple.
3 Seeing Peter and John about to go into the temple, he asked to receive alms.
4 And Peter directed his gaze at him, as did John, and said, “Look at us.”
5 And he fixed his attention on them, expecting to receive something from them.
6 But Peter said, “I have no silver and gold, but what I do have I give to you. In the name of Jesus Christ of Nazareth, rise up and walk!”
7 And he took him by the right hand and raised him up, and immediately his feet and ankles were made strong.
A second usage in Acts 8 also makes the same connection in somewhat different terms:
18 Now when Simon saw that the Spirit was given through the laying on of the apostles’ hands, he offered them money,
19 saying, “Give me this power also, so that anyone on whom I lay my hands may receive the Holy Spirit.”
20 But Peter said to him, “May your silver perish with you, because you thought you could obtain the gift of God with money!
21 You have neither part nor lot in this matter, for your heart is not right before God.
22 Repent, therefore, of this wickedness of yours, and pray to the Lord that, if possible, the intent of your heart may be forgiven you.
23 For I see that you are in the gall of bitterness and in the bond of iniquity.”