The brake lights do work with the ignition off. ~Take off the bulb holder in the back and check all hte connections, then check on the bulb connection itself, could be shorting cos of a funny bulb, or a funny holder. Obviously do both sides! Then follow the wire through to find out where the earth is located (left hand side behind the panel) Check they all attched to it properly etc... If you have a high mount, or any modifications check this too.
If this fails, check the operation of the switch located behind the pedal. Could be broken and when you break, it shorts? Could also be the fuse box itself... Finally check the potential across the terminals while someone applies the brakes, and the current.
