[Ron61]

You can eliminate the neutral safety switch by just wiring around it where it goes into the transmission. I did that on mine and it wasn't the problem. Possibly a loose ground, but then I don't see why moving the shifter would make any difference. My first guess from the way you have explained it would be the neutral safety switch or the ignition switch itself. Sorry I can't be of more help. My problem was in the solenoid itself.

Ron