I'm having a very similar issue with my cab. When I turn on the A/C button, it cycles hot and cold air. I hear a clicking noise, maybe from the footwell. It's hard to tell.
First off, It WAS blowing hot air when the A/C was off almost all of the time once the engine was warmed up. I replaced the heater control valve, the old one was very sticky and hard to move. That actually solved the "hot air blowing all of the time" problem. Shout out to Clark's Garage...
Now I think that there were ultimately two different issues, and I've eliminated one. I think there's an issue specifically with the solenoid while the air is on. Does the solenoid connect to the head unit? Has anyone does a test or had the same issue/replaced the solenoid? It's part #
944-659-215-03
May 21 2018: Here's where it gets interesting, in addition to this post. I continued to troubleshoot. One thing I noticed while driving the car yesterday...the mixer flap is moving by itself. I can see it opening and closing, without touching any of the controls. Here's the catch, the mixer clip is NOT broken. What in the world? I have a used Denso actuator for the mixing door/flap. Maybe I'll change that first. We'll see. If that doesn't work I guess it has to be the control unit or the heater solenoid. Like above, I'm starting to feel more confident about the control unit at this point if this doesn't fix the issue.