Reverse Lights Not Working

Okay, the switch is the three prong thingamajig that plugs into the transmission. What my mechanic changed was the "plastic prong" that has three wires coming from the engine wiring harness. The old plastic prong was the original from 1974 when I bought the car, and it kept falling off the switch that correctly in the transmission. However, the old plastic prong worked properly prior to replacement (when connected the backup lights worked).

I have been to several parts stores. They can find the switch that plugs into the transmission, but they don't find the "plastic prong". What is the correct name for this prong, and could it be the wrong item for my new switch?

Are they readily available?