The timer will only work on "timed dry" and "fluff air", not on "delicate or permanent press. I'm assuming that the timer motor is supposed to get it's power from another source during the non-working cycles , but I can't find a wiring diagram.
The model # is old and doesn't come up in many searches, but any model that's close will probably be helpful. If it helps, the dryer is one half of a "thin-twin combination unit.
Any help will be appreciated.

Here is a manual for a "Thin Twin" perhaps it will help.
It is a bit of a wild guess.
https://secured.whirlpool.com/Service/SrvTechAdm.nsf/2cd44500d572193285256a45004fd9d6/7d322131b309497a852571ca006ce7d2/$FILE/L-56_4314124A.pdf

See page 28
All test done with the unit unplugged.
In auto modes the timer gets power through the heating coil when the coil is shut off.

1. Check the resistor. Looks like it should be around 4500 ohms. It drops the 240 volt heater voltage down to 120 volts for the timer motor. Usually they are mounted in the control console.

2. Disconnect both sides of the heater coil and measure it. Should be about 12 ohms. Then measure from each sde of the coil to the case/frame. Both should be infinite ohms.
What can happen is that the coil can sag or break and touch the case it then will never shut off totally and the timer motor never gets voltage.

3. Check that the OR/TM timer contacts close when in an auto mode.