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If the clicking noise you are hearing from the rear panel in your Mountaineer is coming from the passengers side, you could be hearing the relay contact opening or closing for the automatic headlights (if equipped), rear window defrost, rear wiper, or a host of other features. Behind the trim panel in the rear passengers side are a bunch of the control modules, including Security and Body Control.
the most probable cause of clicking on rear brakes are weak return springs or a broken one.
heat/ac actuator
No, the rear defrost is just an electric grid on the rear window. No air movement involved.
Probably a damaged gear or bearing.
Apparently it is the rear air "blender" ( whatever that is(?)) My 2003 Explorer was making the loud clicking sound from the rear driver side above the rear left wheel. I lived with it for a month before I just found the answer on the net. I turned off the rear fan control (from the front controls) and the clicking has stopped. I guess there is no more air from the rear now but the clicking has stopped- Car is long been paid off and I'm happy again.
If it is in the rear end you need to change the third member oil.
Rear defrost - One side or the other, screws to body at back glass.
The 2005 Chrysler 300 rear window defrost relay switch can be found beneath the drivers side dashboard. The rear window defrost relay switch will be near the center console.
I have same issue except I am on cold and get clicking when attempting to go to heat. also rear areas have heating or cooling
rear air unit has a air blending door solenoid, and is probably out. or broken making a clicking noise
rub it