Electric

That is the classic symptom of a bad ground. To verify that, the left brake light will not turn on at all if you remove the right brake light bulb.

Please list the pertinent information asked for so I can look up the correct wiring diagram. I would figure out what to look for if I was standing next to the car, but being unfamiliar with it, I need a diagram to give you the right information. I need to know the engine size, type of transmission, and for Honda's, the exact model, meaning "EX", "LX", or "SE". Also need to know if it is a two or all-wheel-drive.

Do you have a voltmeter or ohm meter and know how to use it? You will need to get to the wiring behind the lamp assembly.

Dandy. If that is a terminal that slides into the socket, your repair might not be permanent. Typically the slide-in terminals corrode and stop making contact. If the socket is clean and free of corrosion, you can buy replacement terminals, but they might have to come from the dealer's parts department. If the socket is corroded, you are better off just replacing the socket. This is an item I would buy new from an auto parts store. You will find replacements at a salvage yard, but why go through all the work for a socket that might be just as bad as your old one? Replacement sockets will snap in properly, but will not use that slide-in terminal. It will have a solid wire attached for the ground.