Justin,
The back up lights are grounded back at the tail panel. All that is needed to make them come on is 12v. The pink wire IS the 12v power wire for the switch/lights. What might be confusing you is the green wire. The pink and green wires are actually the same line that provides 12v to the lights. It just changes colors along the way to the back up lights. They just cut/broke that line to put a switch in the line to open and close the circuit in order to turn the lights on and off. If you find and touch the pink and green wires together(with the key on), the back up lights should light up. So once you find the pink and green wires, all you need to do is add a length of wire to each one long enough to reach the new switch mounted on the shifter. Assuming, that is, if you're getting the one from summitt above. Just connect one of those wires to one side of the new switch and the other wire to the other side of the switch and you're done. It doesn't matter which wire goes to which side of the new switch either.
Do you have a meter or test light and know how to check for 12 volts dc? I thought you did.
Yep, according to the chassis service manual wiring diagram, the pink wire originates at the "back up" fuse in the fuse box. It then goes to the turn signal flasher and continues on and goes into one side of the back up lamp switch and ends there. A light green wire comes out of the other side of the back up lamp switch and goes to the main body connector and then to one of the back up lamps. Again, this is the same 12v supply wire that started out as the pink wire.