2009 lincoln mks

I have that same problem on my MKS

tapping sound under the dashboard is the AC/Heater system accuator which is defective. Ford/Lincoln has had this issue for years and years. Have the actuator replaced under the dashboard. The actuator opens and closes the heater/AC vents to direct more or less hot or cold air in the cabin. You can test the theory by setting both driver and passenger temp controls to the same temp (i.e. 65 degrees). Then, increase one temp by 7 or 10 degrees, while leaving the other at 65 degrees. In a few moments if you hear the thumping sound, the actuator is attempting to close the AC vent on one side to try to slow the cold air on one side. The thumping sound is the actuator trying to function (essentially trying to close) but the failure results in a thumping sound.