Maytag Auto Dry doesn't work

Dryer works fine on timer only but will not heat and the timer doesn’t advance when set on Auto Dry. Does this indicate a bad control thermostat?
Thanks in advance.

Here are your parts includes wiring diagrams
http://www.appliancepartspros.com/partsearch/modelsearch.aspx?model=PYET344AYW

Note that the diagrams have some of the right side cut off. The second wiring diagram is better just note that the far right line goes to L2.
Also it has the timer chart which may help you troubleshoot this.

Does this indicate a bad control thermostat?
Probably not as the unit uses the same thermostats in both auto and timed dry.

Very strange symptoms.
In timed dry the timer motor gets power directly from Neutral and L1 (120 volts).
In auto mode it gets power from L2 and L1, through the heating coil when the heater is shut off. The 3.77 Kohm resistor then reduces this to 120 volts for the timer motor.

I am sort of stumped on this one. I would have thought it would be the L/H timer contacts but they do not supply power to the timer motor so would not cause the the timer to not advance.
My guess would be the timer but for the life of me I cannot figure out what scenario would give the symptoms you see.
I am assuming this unit used to work OK and it is not a used unit that you have purchased.

Hopefully someone else will jump in with a solution.

Is there a sensor that tells it when the load is dry enough?
No.
The way it works is that in auto modes the timer is advanced only when the heating coil is off. The idea is that as the clothes/air get dryer the heater will take less time to heat the air to where the thermostat shuts off so the heater will be off more as the clothes get dryer.

Often if it is taking a long time to dry clothes it is a dirty vent system, vent louvers not opening fully or a dirty blower wheel.

Gotcha! I’ll take the vent hose off and do a thorough cleaning inside the dryer with the Shop Vac, as far as I can reach. Thanks.