Have a similar issue though mine is a 95 with an nv3500. On my trans the switch is on the drivers side of the trans forward of the speed sensor. I tested the lights by pulling the connector off the backup switch on the trans and shorted the wires on the connector, my backup lights came on. This ruled out the wiring, fuse and bulbs. I pulled the switch and tested it, that was bad. Replaced the switch, tested the switch before I put it back on to make sure it worked but after connecting all of it back up, reverse lights didn't come on. I'm thinking there is something broken inside the trans that presses against the ball bearing on the end of the switch. You may just have a bad switch though.