I havent troubshooted the e30 version, but on the e28, it was a magnetic valve. Had 2 leads, one always 12v and the other was dependent on the switch. I would study the ETMs to see how it wired, but your basic theory in my opinion is bad. Also when you turn the knob to heat, the flaps should also turn inside the dash above the heater core. I know on my if I have the blower on and spin the knob to heat and back, I get crap, like old foam debris out the vents. This tells me that the vents are working which might say the knob is ok. On the e28, my knob was bad and you could test by resistance coming out of the knob.
Hope that helps out and good luck.