The reverse light switch connections are sometimes the failure point.

There are two wires to it, and (at least on my 1983 24GL) each wire had one of those round female connectors to fit over the tips on the switch. The connectors were gooey bad from their oily environment, and were no useless.

Check also the wires from the shifter well. They can lie on the tranny, get hot and the insulation melts and grounds out.

Check these first before going to the trouble to replace the switch.

Getting at all that may require raising the car on ramps and lowering the tranny a little.

Good Luck,

Bob

:>)