I mentioned the resistor because before it didn't make sense to me. Then, I noticed a similar behavior on my Mazda. Mazda deployed aluminum fins on the resistor and it sits behind the cabin filter. I doubt that Toyota placed it inside the cabin filter, but if it gets too hot, it will shut off the flow to protect itself. Need to pull it out and examine it.
On my corolla, which is an 06, it faces towards the engine. I've pulled mine out and examined it when I lost air flow. Not entirely sure why the flow started again, but I could not reach the heater relay. Instead, I swapped the horn relay and fan no.1 relay. It didn't work at first, but then when I pressed down on the relay, it worked.
If you have a chance, look at the wiring diagram for the circuit and there should be some pwm wiring network since yours is auto climate control. My Mazda is auto climate controlled also and does have a pwm network.
Hope this helps.