Is it possible to replace the taillight bulb socket in a 71S? Looks like they are crimped and this socket is damaged to the point that the nubs won’t lock in. I had first thought that it was because the springs were compressed but it’s the actual socket itself.

 

What is a twilight bulb?

 

Taillight bulb sorry

 

You are referring to a standard 1157 socket I believe. The tail light is a dual action bulb (instead of a 1156 single action).
I've replaced both on more vehicles than I can remember I've owned - they do rust out, and go bad.
There should be numerous types available with several different attachment options. The attachment options would apply in determining just how much damage, rust etc. is around the standard attachment point of the 1157 socket. Some get really bad. Yes, you can remove the entire 1157 socket and replace w/ a new socket.
I would generally snip the wires at a good length which you can work with so you can easily reattach the wires with good wire crimp splices and be sure to use some rubber heat shrink wrap around your splices. Pull out the old 1157 socket, and insert the new 1157 socket. It should more or less 'push' in or 'snap' in, if you will. Do a search for 1157 sockets & purchase the one most appropriate for your needs.