I'm thinking a really high resistance connection, or a loose/missing ground may be the culprit, if it takes a bit before the breaker kicks.
Typically if you have a dead-short to ground, the breaker will pop immediately after turning on the circuit, but with most anything else you'll get a sizeable delay until the circuit gets hot enough from the resistance to pop the breaker.
Have a good look at the ground wires where they connect at the headlight buckets on each side. They may be rusty and/or loose.
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