Right brake light won't work and once it's fixed left brake light won't work

Have you tried running a new ground for both lights?

I haven't because the grounds in each light are three bolts that secure the rear light assembly into the body. And once I cleaned all the bolts and all the holes they were going through I thought it would be enough. If it's not I guess I can drill through the assembly and the body and put a new screw in. I just don't understand why as soon as one starts working the other one stops.

Electricity is a funny thing. If you have a bad ground, it could be seeking ground through a different passage. If it isn't too much work, I would try giving both lights a new ground to see if that takes care of the problem. Or, check to see if continuity is lost through the ground of the light that isn't working.

Ok finally figured out that the grounds were good but the brake lights would alternate working based on which side the turn signal was last turned on. I think that means it's a problem with my turn signal switch but I wanted to make sure if you agreed before I actually bought one.

That's a tough call for me without testing it. It could be, but I really question it.