Left side brake woes

I used 3 jumper wires with alligator clips from the light socket to the trunk latch. I've also got tail lights working properly without the additional grounds.

The light socket has definitely seen better days, though. Does anyone have a part # to reference for correct replacements?

You said light socket, but you need to ground the bulb base and try it.
The sockets can loose their ground to the housing.
Tail lights working doesn't necessarily tell you for sure that the brake light is getting the ground it needs.
Some the sockets are so sketchy about grounds that I even solder a ground right to the bulb base itself.