That is a weird set of results. The resistance started at 100 ohms? That is only 120 mA, which in no way constitutes a short. And is nowhere near enough to overheat a connector unless the connector is barely making contact with the wire. Did you tug on the wires going into the two halves of the connector? Occasionally a poor crimp happens.
But then the resistance went DOWN to 50 ohms when you pulled the bulbs? Strange. To me this vaguely suggests that the problem is in one of the fixtures - something moves as you wiggle or remove a bulb. There are a lot of sharp edges in the aluminum skin under the fixture, and poor riveting within those (cheap) light fixtures.
This is in no way a definitive diagnosis, so don't take it as such. But as I say, those are weird symptoms. I guess my primary thinking aligns with yours. Somewhere there is a real short to ground - maybe 1 ohm, which might be enough to overheat a connector, but would not blow a fuse. But then, when you move the wire a tiny bit, the short disappears. This will be a challenge. Good luck.
Bill
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