90% of the time an exterior lighting issue is a grounding problem. RVs are notorious for bad grounds. Using a test light at each light fixture is the best method. 12 volt systems are pretty straight forward - if your test light says there is power at the lamp and it does not light than the ground is bad. Could be as simple as a loose or rusted screw. Usually each light fixture has it's own ground.
Get a test light and a roll of 12 gauge wire. Hook the wire to the negative side of the
tow vehicle battery so you have a good ground, then connect the ground side of the test light to the wire. Connect the trailer pigtail and turn on the tow vehicle lights. Go to each trailer light and check for power now that you know you have a good ground. If there is power at the lamp and it does not light than the ground is bad. If there is no power with that good ground to the tow vehicle battery then you have an open (break) in the positive wire before it gets to that light.
In spite of my first statement above, one light working and all the others out makes me think there may be an interruption in the positive feed. Those lights may be in series and a broken wire will kill all the lights downstream from the break. Quite often you can see a lot of the wiring from underneath the trailer.
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