Brake Light issue

If your third brake light works when you step on the brake, it is probably not the brake light switch. Have you inspected the bulbs? Some dual-filament bulbs can have a single filament burn out. If the bulbs are ok, look at the condition of the sockets.

I agree with Andy Y, but it does seem odd that both rear brake lights do not work. (Doesn't seem logical that brake light switch is bad, if third light works.)

it's in the blinker switch. You have to replace the whole thing.