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Those thermostats have a metal coil with a glass bubble on the end. Three wires stick out of the glass bubble. Follow the wires away from the bulb an cut it loose on the far end. I dont remember off the top of my heat which wire is which but 12V power goes in to one wire an out another to the light. The third is not needed. Other light wire is grounded or goes to the negative of your battery/power plug. If you wire it wrong it just wont work right, no harm, no foul. The wires can only handle about 5V DC so a 1157 tail light bulb is perfect. If you replace the light with a relay you can then run 110V AC threw the relay. I have ran over 1800 watts that way....
Make sure to tape the wires back to the middle of the thermostat leaving some slack. If the wires are pushing or pulling on the glass bubble at all it wont work.