I have a 72 swinger (4 light bumper). Had the original bulbs in it (52K original miles) and the sockets were very corroded and had to dig each bulb out. Got all but the driver side backup light working. Cleaned out all the rust from the socket, checked with test light... that works, and unhooked it from the pigtail in the trunk, test light works there too. The bulb does not light up even when I wiggle it around. Tried a different bulb and still does not light up. Any ideas?

You have fire at the bulb base contact. bulb is good. You have a clean socket so likely contact between bulb sides to socket sides. You now need continuity between the socket & the body back to the batt neg, might be screws/might be direct metal contact

Ive had them where the small brass part for power is sunk in the plastic or worn down as to not contact the bulb part.I usually pull them out of the plastic a bit and try to make them stick out further.Ive also had some where the socket isnt touching the bulb brass for ground.Try slipping a real thin screwdriver thats grounded between the bulb brass and the inside of the socket and see if it lights.Rocky