Rick, I'm not following on how the push-pull switch would not activate in both park and reverse, UNLESS it was mounted 90 degrees to the shifter so the shift arm only activated it while in reverse.
Initially, because of space constraints, my mind went to the switch being on the park end, rather than on the side, for a push-pull, because they do take up more room than a microswitch. Thus the conclusion it would activate in both park and reverse.
A person could get around the "on in park and reverse" by using two switches. The second would be a normally closed switch and would open when you went to park the position [circuit]. The reverse would be a normally-open switch and would be closed in both park and reverse.
More of a pain to deal with (two switches), but still pretty simple, electrically speaking.