[OUChevelleSS]

The car is a '71 SS. The light has worked for a long time before but luckily my mom was driving behind me and caught this for me. I can have my lights on and the back tail lights come on, but the leftmost light where the brake/signal is does not come on when the brake is pressed or the signal is turned on. I checked all other lights and everything else is functional, and I checked with lights on and off. Does this just mean the bulb is bad? Thanks.

 

[Dean]

probably a bad bulb or corroded socket.

 

[ASB]

Bad ground to the taillight socket

 

[John_Muha]

I've had to change both my brake sockets. First the left one then about 4 years later the right. The ground or the crimp at the socket ground failed in each one.
You probably won't find exact sockets for the 71/72 unless you check with Year One. However, it is possible to use any "3 finger" GM brake socket if the dollars are tight.
What's a little unique about these is the socket is sealed to prevent moisture from getting in on the backside. Find another socket from the auto parts store or off a later GM car that had them inside a non-leaking trunk. Notice that that socket is the same diameter and has the same three holding "fingers"?
Seal the back of the socket with a lot of RTV and apply a small bead around the socket face. Let the RTV dry.
The brake socket can be fished out without removing the bumper. Use a long nose pliers and twist the the holding fingers. Reach up underneith the bumper and pull the socket down and towards the side. Cut only one wire off the socket. Strip the insulation and solder and shrink sleeve tube that one wire to the new socket wire. Doing them one at a time prevents the old socket wires from falling back under the bumper. It's easier for two people to re-install the new socket. One to hold it back up inside the housing and another to turn...but did both by myself.