If it was a discrete LED you would be correct, but in this case the "LED" bulb consists of a circuit that contains LEDs. The circuit can be (and in this case is) set up such that the polarity of the source doesn't matter.
I just bench tested one of the bulbs. It lights when connected directly to a 12v battery in either polarity configuration.
I guess that gets me back to a problem with the wiring or switch. Is there any good way to get to the inside of the steering tower to troubleshoot the switch?
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