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From your post it sounds like the unit runs/shuts off OK in timed dry but the timer does not advance i auto modes.
On most units the timer motor gets power through different paths depending on the mode so something in the auto mode path may be the problem.
Check in the control console for the wiring diagram as it will be a big help diagnosing this problem.
Some units use a moisture control board. If yours does clean between the metal sensing strips.
Some unit advance the timer in auto mode through the heating coil when the heating coil is shut off.
Check the heating coil.
Unplug the unit and both wires to the coil.
Check it with a meter, should be around 10 to 12 ohms.
Then check from each side of the coil to the case/frame, both should be infinite ohms (open). If not the coil may have sagged or broken and is touching the case. This can cause it to run all the time.