The question is, are the front parking lights also off or just the rear stop and taillights.
Taillight power goes through the Tail fuse and is turned on/off by a relay via whatever switch is in the car. The front parking lights are also on this same circuit. Thus, if the front lights are on and rear lights off, the problem could be in the rear wiring of the car. This would be even true if the stoplights do not work as the wiring is bundled together. Also look for a bad ground.
Stoplight power goes through Stop fuse and stoplight switch at brake pedal.