No high beam drivers side
May be a burnt out bulb. Replace the bulb.
Sounds like your feeding current back through the system when you plug the trailer lights in. Do your headlights have a single bulb with high/low beams? If so, the bulb is probably bad on the side that does not work on high beam. When you plug the trailer in, it is most likely sending current to the high light (low beam) and that is what you are seeing not the high beam light.
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