Help with reverse lights...

OK for automatic trans builds, the reverse lamp switch was once inside the cabin. A connector below the steering column attached to a switch there or a harness extension cord attached to that connector to reach the floor mounted shifter switch.
In mid 1968 the reverse lamp switch moved to the NSS on the trans. So the 2 wires were routed out through the bulkhead connector.
I suggest a factory wiring diagram. I know purple/violet is correct but is white? I was thinking one violet and one violet with white tracer.
If you have the 3 pin NSS, the 2 outer pins are reverse contacts ( neutral safety in the center ). Which reverse wire to which outer pin doesn't matter.
Temporarily disconnect the shifter so that linkage and detents are no a player. Put the trans in reverse and check for closed circuit, zero resistance from pin to pin. Proves switch and rooster comb good. Route the correct wires to it. Tape them with the brown NSS wire. Reattach the shifter, tune shifter linkage and/or its detents to match the rooster combs detents.
This is what we do when we put a later model trans in a pre 68 build. Cost is a lot less than repairing our interior mounted reverse lamp switches.