Welcome to the forums. Maybe the recirculation door on the HVAC is sticking or the actuator is failing? This can make a 'click-click-click' as the plastic gears may be stripping.
A few moments after shutting the car off, the recirc door will close to keep varmints out of the car and you may hear the noise again. It is over on the right side of the HVAC housing.
This could be a mechanical, not an electrical issue. If you can remove the actuator from the HVAC unit, move the blend door by hand. It should 'flop' back and forth easily from stop-to-stop.
Internally, the actuator plastic gear reduction may be stripping and is damaged. In this case replace the actuator and recalibrate the doors. I believe that all door actuators are the same part number. OEM is suggested for best results.