When was John Mark from Acts first identified as Mark the Evangelist?

I know our Gospel of Mark is anonymous, and I am trying to understand where the traditions of attribution come from. As far as I understand, the tradition is that the Gospel was written by Mark the interpreter of Peter, who would also be the John Mark referred in *Acts of the Apostles* as a companion of Paul who split up with Barnabas at some point. As *Acts* does not state that John Mark became an interpreter of Peter, I assume these are two different claims: - **Claim 1:** "The author of Mark was the interpreter of Peter". - **Claim 2:** "The author of Mark is John Mark, the character from *Acts of the Apostles*". I know that we can trace *Claim 1* one to Papias (though we do not know if he's discussing *our* Gospel of Mark), and later to Irenaeus (who is definitely talking about our Gospel of Mark). But they do not seem to indicate that the author was also John Mark from *Acts of the Apostles*. I have failed to find our first source for *Claim 2*. **I am interested in finding out at which point in history people started assuming that John Mark (the character in *Acts of the Apostles*) is the author of our Gospel of Mark** (or, failing that, at which point people started assuming that John Mark from the Acts of the Apostles became later in his life an interpreter of Peter).