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What's the parts diagram say ? Typically w/ assembly the "lightbar" is a separate part inside a housing ... many are just a sealed lightbar/ lens. Have never encountered a set up with ability to switch out an individual LED. If the whole bar is out -- look for some other problem. If it's just one LED .... e-bay get a used one.
I put the light back on just to drive around while I waited for a new housing (that I luckily hadn't ordered) and it just started working again.
While removing it I noticed one of that connections was slightly janky, so I'll assume it was that one. I got rear ended a while ago so it was probably the body shops fault.
that's probably true, the body shop didn't fix it correctly. Make sure you fix it securely and not rely just on chance. the brake light is crucial to your safety!