Luke's sources for Paul's early biography

There's talk that Luke took Paul's dictation.

Luke's use of the Gospel of Mark (wholesale) hints that, before Paul, Luke didn't have firsthand access to Jesus' first generation of followers, nor even second. The Apostolic era is later, so those generations were accessible to Luke. But here, too, he could find documents - not least, letters attributable to Paul. Luke was not a muhaddith like Papias; Luke had a bias to written texts over oral tradition.

Paul did on occasion speak of his own past: such as in Galatians 1:13f, and in a (probable) "severe letter" now preserved 2 Corinthians 10-13 [UPDATE 12/12/23: I now think the Lachrymose was different so not preserved]. Some of these episodes end up in Luke's Acts. Let's talk Gamaliel as a test-case.

The Christian historian Luke holds Gamaliel as an important rabbi among the Pharisees; tending to moderation. This is in accord with the Jewish memory, as preserved (mainly) by Gamaliel's students. Luke also claims that saint Paul né Saul of Tarsus held himself out as a devotee of Gamaliel. THAT, I don't know.

Gamaliel's name is nowhere uttered in Paul's epistles - even in the disputed epistles. It also seems strange that on the one hand, Luke has Saul as a persecutor of Christians; and on the other, as a Gamalielite. Wouldn't such a one be a moderate? I mean, it is possible that Saul vacillated over his career in Judaism, before converting, but . . .

Pauline epistles survive in which the narrator declares himself an ex-persecutor; Galatians is the most important. If Luke had access to such, and to letters of Paul (or to Paul) as mentioned Saul's training as a Jew, he could reconstruct the events as he had.

But that doesn't mean we must. Can we trust such letters, not preserved to us, were authentic? 1 Timothy is not taken seriously by Paul's biographers; its narrator's self-image famously contradicts 2 Corinthians'. Pauline apocrypha went out early: also dismissed are 2 Thessalonians and Colossians.