A few weeks ago I asked aloud on Facebook why it was that the Apostle Paul never mentions John the Baptist. Several responses were given, and many satisfactory at one level, but not in a way that settled the matter for me. I guess my question is the prelude to another one: did John influence Paul at all? Directly? Indirectly? Paul's apocalypticism with a strong emphasis on judgment and deliverance, his eschatological pneumatology, and his one time baptism for initiants seem to me to connect Paul back to John, though maybe not directly.
J. Ramsey Michael's "Paul and John the Baptist: An Odd Couple?" Tyndale Bulletin 42.2 (1991), 245-260, explores this question. First it looks at the "Lukan John" and "Lukan Paul" of Acts before diving into a references in Paul's epistles that may show reliance on the Baptist Tradition. In my opinion the data from Acts is more interesting for showing how the Lukan tradition wants to connect Jesus to John one direction and to folk like Peter and Paul in the other direction. Acts 19.1-7 has the important function of showing that the Jesus Movement is grounded back in the prophetic ministry of John and continues in the apostolic ministry of Paul. Acts has been dated any time from the 80s to the 120s. However one looks at it, John is an important figure some five to nine decades after his death and for Luke it is important to connect Paul back to John just as he connects Paul to Jesus.
I presume Paul didn't need to make this connection explicit either because his preaching may have said all he needed to say about John (if anything at all since his vision of Christ seems far more concerned with the post-resurrection manifestation) and/or because the circumstantial nature of the epistles never required any appeal to John (contra the gospels and Acts).