He's more of a traditional Republican, except he's even more of a fundamentalist Christian than most of Republicans. And, I think he was convinced to join the Trump ticket because he knew that Trump would probably get himself impeached. Being Vice-President to Trump is the golden ticket to a seat at the Resolute desk.
Pence is the one directly implicated by the resignation of the NSA guy. He was tossed under a truck in the resignation letter. If Trump goes, he goes.