2003 Dodge Caravan rear lights

The way it is wired, a single circuit bulb in the rear would be the most likely reason they would not work. Two circuit bulbs must be used or the rear brake and turn signals may work but with no filament the parking lamps will not. See if the front bulbs are the same and switch em to check, or recheck the bulbs you have replaced. Ok I know it is unlikely but check that first before any other testing, I Will look into this tomorrow further, ok.
The only other thing could be a wiring open in the trailer wire, if so equipped. Or just an open between the module under the hood and the rear lights. Do your hazards work in front?