I am having trouble with my tail light sockets on my 68 cutlass. For some reason the sockets are loose and the tail lights wont work properly. Is there something that holds the sockets in place, for on each side of where the tail light sockets mount are 2 posts. Am I missing something? for the tail light sockets keep coming loose. Any and all help will be much appreciated!

 

They simply push in pull out. Check the metal ground tab and plastic tabs. If they are broken you need to replace the socket. You could try to pry up on the metal tab a little to stretch it back into a usable position. It is the likely source of the intermittent illumination(lack of a good ground)? Also, check the cast metal housing for damage. Replace as needed.
The sockets may be available from a wire harness supplier or you may need to purchase a rear harness assembly and just replace all of the 50-year-old wiring back there. I didn't see them in the Fusick catalogs but that doesn't mean they don't exist. Dorman may have them? the housings will need to be sourced as used parts.

A quick google search produced this:
https://www.carpartsdiscount.com/tai...html?3594=3155

And this although it states "twist" which is not the case on a 68.
https://www.opgi.com/cutlass/PZ00306/

 

Make sure the spring loaded lamp contacts move freely and contact the lamp filament contacts. I've found that corrosion builds up around the wires and does not allow a completed circuit. The tabs on the socket that secure the lamps sockets to the housing can be adjusted so everything fits snug.