Hey, I am using a '70 Torqueflite, and reverse light acts strange. It does switch as needed, I can sense the voltage coming on when it is in propper gear (measuring with voltmeter from bulb socket), but bulb won't light. If I remove the socket from transmission and short the contacts, then it lights. What can it be? It is like 'not having enough power to light the bulb', but has enough to give a voltmeter reading. Is it common?
You are onto the source of your problem. The three wire connector on that trans uses the outer two wires for the reverse lights. The center wire is grounded in Park and Neutral for the starter relay ground connection. I would try a different switch in that trans. If it still doesn't work, it is possible the plastic actuating cam on the rooster comb arm was broken by someone installing the valve body carelessly, or there is a mismatch of different year parts in that trans - 1968 and earlier are one style (no plastic cam, just two metal humps on the arm), 1969 and later are different parts - and they don't interchange.