Who watched Stephen being stoned?

Surely the author of Acts of the Apostles could not have seen Stephen stoned, since the event would have occurred before the author was born, as Acts seems to have been written some seventy years later, around the turn of the century. Yet Acts is so detailed and dramatic in its account, that the impression is that it was written straight after the event by an eyewitness.

Acts says that Saul, later to be named Paul, witnessed Stephen being stoned, but Paul himself never mentioned this event. Bear in mind that only Paul would have been able to pass on the knowledge of his presence at the stoning so many years earlier, so his failure to do so must raise doubts about Luke's source. In fact, scholars have even called into question the claims made in Acts that Paul spent his formative years in Jerusalem.