I'm not so certain about that. In John 18, Pilate has Christ brougbt into the palace, away from the jeering crowd, where Pilate had what is commonly referred to as an interrogation, but reads more like an intimate theological debate. John documents their exchange in the kind of excruciating detail that could have only been known to somebody who was present. So ask yourself, who wrote it down?
Presumably the only persons present where Christ, Pilate, and perhaps a small handful of guards and advisors. One of them recorded the exchange with the specificity that could only have been known to somebody present, and found cause to relate that account to the author of the Gospel.
Not disputing what you said. But interesting that you postulate it was Pilate.
No record, such as in Acts, of Pilate’s coming to Jesus, like Paul on the Road to Damascus. Or he death.