If I remember correctly the coolant light warning should be off when the circuit is shorted so that way the light would come on if the sensor gets disconnected or there is a break in the wiring. I think also that it is controlled by the LCM and not just a wire to the bulb on the dash. I would try shorting it out at the connector. You could also do some testing on the cooling switch to verify how the system works.

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1988 325is (purchased new) sold
2004 X5 3.0 2005 X3 2.5
2008 X5 3.0 (new to me)