Like Rick suggested, I was going to suggest a "mometary on switch," like can be seen at
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You could mount the switch, then run a spring through the shift handle.
The spring would cause the backups to come on in park and neutral, so you'd want it to be key activated.
Another option would be, a microswitch, which got pressed when the shifter was in a reverse or park position.
That could be modified with a bit of scheming. For example, one set could be to activate the micro switch by a cam, so it was only pressed when in reverse (e.g., a high point would activate the switch, then, when the cam dropped off, as you went to park, it would open the circuit again.