All those lights you mentioned have nothing to do with the ones you have that do not work and "having power to the rear" means nothing. Tail, "marker", and license plate lights are all connected to the same power source, the headlight switch but have separate fuses from the headlights. Grounds and power can be tested at each light socket.
Trailer plug connects into each circuit and can short out them too.
Trailer plug connects into each circuit and can short out them too.