So I got a '57 Plymouth that has an automatic push-button transmission and I can't leave it unattended!!! Every time I park and push it into neutral it stays there for a moment then jumps into reverse!! It won't do it when you first start it.. You have to start it shift from another gear then back to neutral. It won't do it while I'm driving, just when I'm parked. Does any have a clue what's wrong??? Or is my Plymouth pullin' a Christine?
You may have motor mount issues and an out of adjustment shift cable assembly. Try adjusting the cable per repair manual, and while u r down there check the mounts. My guess is that the rear mount may be completely gone and the transmission moves, causing the transmission to go into reverse.
Dad had a 62 dodge with the same problem. He always said it was the park cable that was adjusted incorrectly but he never tried to adjust it. He was good at getting out quickly and sliding the brick under the tire before it could roll very far.