no back up lights

Easiest way I've found is pull the harness connector off the switch and poke the legs of a cotter pin in the 2 holes. If a test light shows the cotter pin is hot there should be lights on at the rear too. If the lights are in fact on, One of 2 problems exist, bad switch or wrong rooster comb inside the trans.
If the lights aren't on the problem is between the cotter pin and the bulbs.
If the cotter pin isn't hot the problem is between the cotter pin and the fuse box.