On page 1560 of the Apologetics Study Bible there is an interesting comment regarding Luke 23.12 and when Jesus died.

"And the same day Pilate and Herod were made friends together: for before they were at enmity between themselves."

Part of the note reads,

"Pilate's fortunes with the emperor were further damaged when his patron, the anti-Semite Sejanus, was deposed by Tiberius in A.D. 31. Pilate's actions in including Antipas in the trial of Jesus may have been intended as an olive branch. But this requires a date of A.D. 33 for the crucifixion, not nearly as likely as A.D. 30."