Another issue on my car was that the upper passenger side tail light was not working at all. In the process of fiddling with it, both of the little spring-loaded contacts broke off and came flying out. I searched around online a bit for replacement sockets, but seems like everything is "universal" and has different diameters. Is there any one in particular that works well for a 72 Cutlass?

In the meantime, what I did was cut a pen spring in half and put a half on each wire. I then stripped a bit of insulation off each wire and built up a lump of solder at the end of each one. I put it all back together and it actually worked! But no idea for how long...next drive could vibrate it all to hell.

 

You can buy a new socket at the auto parts store, take out the parts and splice the wires with the brass end piece into your existing harness. (I used heat shrink over the splices) Used a dremel tool and some little wire brush wheels from harbor freight to clean up the sockets... mine were rather crusty! The glass bulb came out but the metal bulb base did not... fun fun fun....