Left side brake woes

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.

I eliminated the socket altogether and made connections directly to bulb shell and filament contacts. Still nothing. I even tried it with jumpers straight off the kick panel connector