Jon, It's possible that the wire cable that comes thru the spiral metal jacket is kinked at the spot where the wire cable goes into the jacket. Tough to get to. If it is at the control end you can get the control away from the dash enough to see it. If it is at the other end you have to stand on your head to get under there and take the the round heater duct off(should have a clamp on it) to get a better look at the cable end.
Jon, It should move freely. The cable moves the lever attached to the flap. Make sure there is no loose felt from the flap stuck on the pivot points of the flap.
I was able to remove the whole "box" on my series 62 without removing fender or inner. loosen the inner and wedge out w a 2x4. My job was easier because I already had the dash cluster removed for repair (MUCH better access!) replacement morse cables are available. Be sure to route cables as removed...pics !! In my case , the elaborate multi door mechanism was just very sticky. Factory grease had turned to cement. I had purchased a complete box and control/cable assy before tackling job. Made the job much clearer to understand .I have available a complete functional heater box and control mech. w cables if u need parts. Includes good htr core and ranco valve. Control set has functional heater blower switch. You will need to replace the special blower duct hose $100, available. Tricky to install. Take your time, lots of pics, good luck , happy skinned knuckles and arms !!