It's no puzzle at all. The blend door either is busted and is flopping back and forth or it's not properly seated on the actuator shaft.

 

I have the exact same issue with my 1999 F-150 XLT. Once the truck runs for a while, I can move the temperature control **** back and forth several times and the switch begins to work. It is almost like it is loosing pressure overnight but then once the pressure in the system builds up it will work. This usually takes 5 - 10 miles of driving before it works. It feels exactly as you described as loose until the pressure builds up. Still haven't found a solution.

 

A new actuator fixed my issue! The old one wouldn't turn until I turned the **** halfway, and then it would turn fast. The new one turns slowly as the **** is turned. I have cool and warm air now!! Thanks for the feedback/help guys.

 

Replaced the potentiometer/temperature control switch and everything is working great now. Thanks you IA Chiefs fan.