Is what broken, the light? Sounds like it's working. What light turned on? If it's for the coolant level, I'd suspect the switch in the coolant reservoir. Most use a magnetic switch and a magnet that floats on a piece of styrofoam. That float may have "drowned" or the switch could be sticking. None of that has anything to do with the water pump.
Thursday, December 13th, 2012 AT 4:56 AM