AC: “I think it was pretty clear to Pilate that he wasn’t dealing with an ordinary man.”
Agreed. While Pilate was probably used to judging all sorts of criminals, he was apparently surprised by Jesus. I’m sure the typical criminal was eager to plead innocence and/or beg for mercy. When Christ failed to defend himself, it was quite unusual. Regardless, I don’t think there’s any evidence that Pilate actually believed Christ was the King of Jews or the Son of God. Christ must have been unusual, but Pilate still had Christ executed. That went, of course, according to God’s will.
Ironically, Pilate was probably blind to Christ's mission and identity for the same reason that many of the Jews at the time didn't accept Him. They probably all figured there was no way the Son of God would come to earth through humble beginnings and wouldn't have any interest in assuming temporal powers.