First off, I have no clue what it is. Try this, when clicking, adjust the temperature control of the driver side. If no difference, adjust the temperature of the passenger side. Possibly a blend door control?

James

PS The reasoning behind this is that I have replaced dozens of blend door motors on Ford products, Explorer and Escape. When the blend door motor goes bad, the temperature in the cabin won't change and the motor keeps running causing it to click just as you explained. On the Ford motor, you are actually hearing two plastic gears slipping because they are worn or stripped.