Hello,
Stay in touch. I was told by appliance parts pro that it may be a moisture sensor. I don't see one listed in my documentation. There is however a timer thermostat, or ? Can't tell from schematic. Schematic looks like a thermostat but has a third line drawn like a reostat/potentiometer so maybe that's it variable on moisture? Anyway I also checked my exhaust hose as it was kinked. My dryer must have been moved around, so I straighted it and it ran the cotton cycle fine. So I will confirm hose fix or not first then replace the timer thermostat if the hose straightening doesn't work.
Yes my wifes likes all the other settings over the timed.
bob

Rawbert
Your unit is Gas whereas rdellinger's is Electric.

If the units do not include moisture sensors they will both advance during Auto cycles when the heater is turned off but the way they are hooked up is very different.

rdellinger's has a resistor in line with the timer motor which reduces the 240 volts (heater voltage) to 120 for the motor during Auto. This may be blown.

Also they may have a dual element. If one element opens and it is the one that provides voltage to the timer in Auto the timer will not advance.

The thermostat setup is also different.