your tail lights and license plate lights run off the same circuit. Everything else is different so doesn't help much. Except maybe headlights, I assume they work, which implies your switch is OK.
Usually, I will blame the trailer circuitry first, as most aftermarket people do a crap job installing it. Even the factory one takes abuse from high obstructions, salt on the road, etc. This usually shows up in the turn signals or brake lights, not so much the tail lights.
There is a TAIL relay which comes on when the switch is grounded, in either parking or head light mode. This relay is under the hood. Should be able to feel it click it times get hard with the other tests below.
hat relay feeds the 10A fuse labeled TAIL . SDS's diagram is correct, but rotated 90 degrees from mine, so be sure to follow the shapes of other stuff.
That fuse then feeds 4 or 5 different directions.
2 of those are your front marker lamps, the little bitty amber ones right on the corners in the front. Check those to be on, check the bulbs make sure they are good (my alarm setting made those bulbs burn out first). Knowing these are working will eliminate the fuse and relay from the search.
The next leg feeds the back of the truck. Rumored to run down the drivers side of the truck, forget if inside the cab or outside. This should be all green wires, going to 2 license plate lights, and 2 tail lights. There are a bunch of wire connectors en route, and a plug in connector. This is the one I worry about most.
Another leg feeds the trailer brake controller, if you can easily unplug it and leave it off for a while, that might be easier than resetting, no idea what a reset will do.
The last leg goes to the speedo, does your indicator light bulb there turn on with the switch? That will eliminate the fuse and relay as well.
Do you have a meter to check voltage and resistance, we can go there next.
Good luck, check back