Pull the connector off of the neutral safety switch and check the two outside terminals with a test light or volt meter. You should have voltage to both terminals with the key in the run position and the shifter in reverse. .
You didn't state this very well. You cannot have voltage at the two outside terminals with the connector off, and there wont' be anything at the transmission (in reverse) except CONTINUITY between the two outside terminals OF THE SWITCH.
As Red said, you can pull off the connector, there will be power WITH THE KEY ON at ONE outside terminal. You should be able to jumper the two outside pins of the connector together and get the lights to work.
If they do, it's a transmission/ switch problem
If they don't it's in the wiring somewhere, a bulbs problem, or a socket(s) ground problem.