Well, you'll need to check for 12V on that wire, but you can also check for voltage on the plug to the motor. If AC there is a relay out on the AC housing, and whether AC or not there is a resistor cluster on the housing as well. You can check for voltage out there as well.
My suspicion would be the heater motor itself or power to that brown wire if you have nothing, as I recall, each wire to the motor gets power based on the switch setting, so unless there is something majorly wrong between the switch and the motor, the motor or brown power wire are the major likely culprits.