Automatic stalls in reverse.

No experience with this one, assuming you are sure it's an electrical issue..... If so, I'd start by looking at the neutral safety switch... maybe swap another one in. You should be able to troubleshoot it's function, and the whip as well... maybe even disconnect the backup lights at the switch and see if you are making any progress.
I have seen valve bodies without clean neutral kill a car in reverse, but not like you seem to be describing.