It's a BAD GROUND on the right side tail light, so power is having to travel throught the tail light on the right side, then to the tail light on the left to find ground.
Turn on the tail lights, then step on the brake, does the right side go out, and the left side works? If so then its the Ground. If both side light up with the tail lights on and stop lights, then yes it could be a bad switch. If the wires were shorted out some place then if would do the same both ways.
