In John 16:4, Jesus tells the disciples that they are to remember the things He told them. I expect that as the writers sat to put down these remembrances, the Holy Spirit released their minds to recall with near miraculous accuracy the things spoken. Just enough discrepancy in the synoptic gospels however to enhance the credibility of their human witness.
They were not God in a trance, but men in obedience.
Which brings me to the mysterious connection I perceive between the conversation Jesus had with Cleopas and another disciple on the road to Emmaus and the book of Hebrews. Jesus filled them with information but withheld His own identity. Could it be that He wanted this information included in the Bible and ensured that by revealing the details of how He spanned the whole of God's covenant with men?
There are interesting details to this story, how Jesus acted as if He were going further, indicating that He was not actually going to Emmaus; how there were two men hearing everything, nothing could be admitted without two witnesses, how Jesus restrained their ability to recognize Him because if they had known Who it was that was speaking to them, they wouldn't have been able to process and retain the information!
Dunno, but my vote, unimportant as it probably is, goes to Cleopas as the mysterious author of the book of Hebrews. Or maybe the other guy, un-named in the text.
No real proof, just a suspicion based on the time I lamented in prayer that I would have loved to hear that conversation.
"Maybe you have," came a soft response in my spirit.
One of my ponders to be answered some sweet day as I snuggle at His bosom!