On my 2010 GT premium with dual zone climate, there are3 or 4 different blend door actuators and there's at least two different part numbers for them. I know some of the climate stuff changed from the 2005-2009 to the 2010+ years, so I'm not sure if your car also has different types of blend doors.

 

should only be 1 blend door, 1 fresh air door, and 1 or 2 mode door actuators

 

The blend door actuator takes about 20 minutes to change and only requires the glove box removal, some tools and some patience.

My 2010 had the same issue when i bought it.

I agree though blend door actuator 100%

I used this pic when i changed mine the red arrows indicate the blend door actuator

 

I stuck my head under the dash and blindly mashed my fingers onto the a/c buttons and turned the key on/off until I could localize the sound. On my car it's coming from behind the center stack / driver side foot well to the right of the gas pedal. One of the auto parts chain told me they are different part numbers and they are all special order.

 

When you get around to replacing it, there may be an actuator door calibration procedure you may have to run. It's like that for 05-10 don't know about 11+.

Found it, yep there is one for 2011+
http://iihs.net/fsm/?dir=977&viewfile=Climate Control System.pdf

page 412-00-45 section K15

It might be worth a shot to run the calibration anyway. It may fix your issue without needing a replacement. This helped me fix my stuck door one time when I used the defrost setting and the vents got stuck on Defrost. I think I've used the defrost setting only a handful of times in AZ.