It might be a (not working well) self-resetting circuit breaker in the line. Look for a small, two-terminal module in the 12V line, one wire in, and one wire out. Probably up close to the battery, or even on the battery post. Sometimes on the frame, too. When the lights are not working, you would have voltage on one side, but not the other. When they are working, you would have voltage on both sides. All voltage checks with respect to ground.
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