+2 on the low voltage at the LED causing the small dim dot of light. Reverse polarity will not light at all. I have rigged up LED's for props and I can get the small dim dot to show up by shorting the 12v with my finger (non sweaty) across the wires so it doesn't take much voltage to get that.
In addition to the wiring checks, the switch could be bad, not making good contact.
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