Hold on there ...
There are two light bulb sockets in the back corner. One is for a single filament 7440 bulb that is the turn signal and emergency flasher light. THat light socket has two wires going to it. The other is for a dual filament 7443 bulb, one filament is for the tail/running lights, the other is for the brake light. This second socket has three wires, with the colors that you found on the replacement socket.
Before you try to replace the socket, make sure you are working on the correct socket. If you replaced bulb in the two wire socket, that won't affect your tail light. Also, if you put a dual filament 7443 where the 7440 should go, you should put a 7440 back in there.
Just be sure before you cut any wires, the two wire socket is turn/flasher, 7440, the three wire socket is both tail and brake, 7443