Reverse lights

You have a shop manual? wiring diagram?

On your car the lights wire comes up into the left kick panel connects to the under-dash harness, and goes up and through the bulkhead connector, and from there down to the transmission neutral safety switch. The switch wire comes back up, through the bulkhead, and picks up switched power, at the radio connector on some cars.

WHY do you need to hook them to the shifter? IF you have a good neutral safety switch now, and it's properly hooked up, you don't even need the switches on the shifter.

Bear in mind that the switch on the transmission is PROBABLY safer, because the shifter can get out of adjustment, and so the trans might be in gear when the shifter is in park/ neutral.