Chevrolet Repair Questions? Ask a Mechanic for Answers ASAP
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Does the clicking noise seem to come from the passenger side of the dash?
The problem is going to be a stripped electric actuator for the a/c inlet door. This actuator controls positioning of the door for fresh air or recirculate mode. The plastic gears within the actuator strip, causing the clicking sound. The dash must come out to replace the actuator. If you just want to stop the clicking noise, you could disconnect the wiring to the actuator.