The 63-66 C10-20 trucks that came with the automatic trans had provisions for the back up lights, the switch was incorporated into the factory neutral safety switch. I had a '65 C20 V8 AT that I bought new for many years, the backup lights were round, located below the tail lights. my '64 has backup lights, it is an automatic also.
From my experience, the three speed column shift transmissions had provisions incorporated into the column for the accessory backup lights. The floor shift transmissions had an accessory mounted switch that attached to the top of the transmissions.
The '67 four speed transmissions, which are the same as the earlier models, but are different from the '68 and later New Process transmissions, have a backup light switch built into the transmissions. Wm.