I have a similar problem in my 2012 Ford Focus SE.
I get a "click, click, click" noise happens with a repeated clicking a bit faster than once a second (maybe as fast as twice a second) when either
(A) I turn the heater/AC fan speed to "0" and then turn off the ignition. The clicking noise commences as soon as the car is turned off. The clicking noise stops if I turn the heater/AC fan back on to "1."
(B) Press the "recirculate air" button for the heat/AC controls. When the control is in "recirculate" mode (dash LED lights), the "click, click, click" starts. The "click, click, click" stops again when pressing the "recirculate" button a second time so that "recirculate" mode is off.
From reading other postings, it seems that the problem is likely with one of the HVAC door actuators having some broken gear teeth and that the proper repair is to replace the broken actuator. I haven't done this yet. It sounds like the repair requires removing the glovebox to get access to the actuator, and then the actuator itself is tricky to remove. Maybe I'll have a go at making the repair myself after Christmas.
Kate1532, are you still having the problem?