Pont. Sunfire Backup lights

My 98 Sunfire's backup lights wont work...fuse ok, bulbs ok, no apparent loose connections. Man at auto parts store says it's the neutral safety switch. True? Has anyone done this before?

It maybe a bad switch in the tranny. when you put it in reverse it turns the switch on so the lights come on. I had broken wires in the trunk that had to be fix so my brake lights and backup lights would work. Sunfires are known for cheap wiring.