If you remove the glove box, you can get a close view of the actuator motor. It sits on top of the whole A/C housing thing, left of the airbag. If you have a small hand, you can fiddle with the A/C temperature dial and hold the actuator to verify if that's your problem.

With mine you can see if visibly clicking and holding it you can also feel it.
The part isn't terribly expensive, like $60, but geez the labor to get this out looks incredible. Definitely a weekend project for me.