Marker/tail lights are a separate circuit from the stop/turn signals.
Is the power out the back of your truck working? Putting power to the right connectors? Easy to tell with a 12v test light between pins 3 (tail) and 1 (ground). Probably $5 at any auto parts store.
Assuming you have 12cDC in the trailer (battery or converter) You can check the trailer wiring when not connected to the truck with a short jumper wire between pins 3 (tail) and 4 (+12v) on the umbilical cord. This connects 12vDC to the running lights -- folks do this when parked at campgrounds to illuminate the exterior of their trailer at night making a midway atmosphere in some camp grounds. A test light between 4 (+12v) and 1 (ground) should light. Note the first is a wire, the second is a light.