I'm still reading Richard Bauckham's Jesus and the Eyewitnesses: The Gospels as Eyewitness Testimony.
Bauckham argues that the Gospel of Mark contains eyewitness testimony that goes back to Peter. Here are some reasons:
1. Bauckham compares the Gospel of Mark with ancient biographies that came later: Lucian's Alexander and Porphyry's Life of Plotinus. In these biographies, certain individuals frame the story and appear often in the course of it. In the Gospel of Mark, that's the case with Peter. In Lucian's Alexander, we see that with Rutilianus. In Porphyry's Life of Plotinus, it's somewhat the case with Amelius, but Porphyry's work here----similar to the Gospel of John and perhaps in imitation of it (according to Bauckham)----ends with an affirmation of Porphyry's own testimony which thus supersedes Amelius. Similarly, in John, Peter is close to the end of the story, but the Gospel then goes on to affirm the Beloved Disciple and his testimony.
I do not recall if there is any place where these authors explicitly say that they are recording the eyewitness testimony of the people they mention, every time that they mention them. On page 135, Bauckham says that "there is one obvious candidate for the source of much of Lucian's account: the Roman aristocrat Rutilianus", which tells me that there is no explicit statement that Lucian makes that he is drawing from Rutilianus' eyewitness testimony. On page 140, however, Bauckham says that Porphyry affirms that he received some information from Plotinus himself and from Amelius, so perhaps Bauckham's argument is stronger when Porphyry's work is considered. Moreover, Bauckham refers to New Testament passages that highlight the importance of eyewitnesses "from the beginning", so maybe he has a point that Peter is placed at the beginning of Jesus' ministry in Mark's Gospel to show that he was a valuable eyewitness and that the Gospel of Mark contains some of Peter's testimony. Why isn't this explicitly stated in Mark? Bauckham says on page 147 that ancient readers and hearers of these works expected for them to have eyewitness sources, and that they were alert to indications that the Gospels provided.
2. There were some arguments that I did not entirely understand. For example, Bauckham notes that, in various scenes in the Gospel of Mark, Jesus' twelve disciples are presented as a group, and then there's a focus on Jesus. Bauckham refers favorably (it seems to me) to an argument that this is based on eyewitness testimony: that it is from an eyewitness account that was in the first person plural ("we"), and that, when it was recorded in Mark, the first person plural was changed into a third person plural. That doesn't strike me as an iron-clad argument. Bauckham also notes that Mark discusses Peter's impressions, and (sometimes) the impressions of other disciples, and he attributes that to Mark's reliance on the testimony of Peter and (in some cases) others. And Bauckham states that Mark's Gospel contains Peter's thoughts regarding his own denial of Jesus, which occurred when Peter was away from the other disciples and was followed by feelings of guilt, which Bauckham believes is reflected in the Gospel (on some level).
I heard some of these arguments when I listened to pastor and psychologist David Antion's summary of the four Gospels. When I told my New Testament professor about the argument that Mark was based on Peter's testimony because it reflects Peter's guilt about denying Jesus, she responded that this was speculative. (And the response in my mind was, "And Q isn't?") I think that there is some reason that Peter is emphasized in Mark's Gospel. It could be on account of Mark's Gospel containing Peter's eyewitness testimony. I vaguely recall a scholarly argument that Mark's Gospel was written in Rome, and so it highlighted Peter, who supposedly was there as a leader of the church, or had been there as leader of the church (before Mark was written).