Dandy. The next best place to start is with measuring the voltages right at the fan motor when it stops running. You should find 12 volts on the dark green wire. If it's missing, we have to look at why the relay isn't turning on. Next, you should see 0 volts on the black / tan wire when it's still plugged in, and the switch is set to the fasted speed, and you should see progressively higher voltages as you reduce the speed. If you always have 0 volts on any speed when the motor quits running, the brushes are worn and the motor must be replaced.
If you find the full battery voltage, (12 volts) on the black / tan wire, there is a break in the ground side of the circuit. Further tests will determine if that is in the resistor assembly / connector or the switch assembly.
If the modes also do not switch properly when the fan stops working, suspect the ground wire that both systems have in common.
Monday, December 19th, 2011 AT 12:05 AM