Cadillac Repair: 2000 Deville, Clicking noise in dash, electric actuator, plastic gears

Question
After starting my car, there is a clicking noise that comes from the middle of the dash.  It usually goes away after several seconds but can sometimes last for minutes.  It is only present when the climate control/HVAC is on & often the lower floor vents will not blow air during or after this sound is occurring.  It sounds as though there is a stripped plastic gear somewhere whose threads are no longer catching.

Any help you could give would be much appreciated.

Thanks!

Answer
There is an electric actuator behind the dash that has plastic gears which control which doors to open for the heating and air conditioning. Most likely the plastic gears within this actuator are stripped and the actuator needs to be replaced. This requires removal of the dash to replace the actuator.