Yes, it should move. There are two lower ones. Does the other work? They do get sticky if you don't move them regularly. There is a push/pull wire inside a coiled wire sleeve. If a little bit of corrosion or detritus get in there, it can bind. If the flap it controls is stuck, that can cause it as well. Don't use brut force. Breaking the lever is an expensive result. does the top left one work well? That one often sticks because the water valve to the heater core sticks. Pack your patience if you decide to go after the repair under the dash.