Chrysler Repair Questions? Ask a Mechanic for Answers ASAP
without actually hearing the noise I can give a best guess, and that would be a mode door, OR blend door actuator.
they are small electric motors that control the heat and a/c air flow direction AND the temp of the air coming out the ductwork , when the motors fail the FIRST thing they do is click that is the plastic gears making noise the fix is replace the actuator, while not nearly as common as they were when electric actuators first started being used they like all motors can fail, now you have a 2012 and MAY still have some factory warranty left (depends on when the car was placed in service) IF you are out of the 3/36 basic warranty and DO NOT have a service contract you can call the 1 800 customer service help line and ask for assistance, BUT depending on which motor failed, the repair may be under 200.00, you may be able to do the repair your self IF you're handy and can comfortably fit under the dash and still work.
as for why the noise is there occasionally with the car off that's easy we do self checks after the car is off and put the doors in a "rest" position so after you shut down the car the computers are moving the doors to their designated "rest" spots.
the best way to determine what actuator(s) has/have failed is with a scan tool that can communicate with the heating computer (HVAC MODULE) if you wish to attempt the repair yourself I can give you a down and dirty method of determining the failing actuator and the procedure to replace it