Old GE Dryer End-of-Cycle Cool Down Not Working
I have an old very-small/apartment-size General Electric dryer that uses a mechanical timer. For the last 5 minutes, it's supposed to turn off the heat and continue to spin just blowing air through the clothes (to take advantage of residual heat for energy savings, and to reduce wrinkling). But recently, the dryer just shuts off with 5 minutes remaining on the timer knob, leaving the clothes hot.
My first thought was that a thermostat or thermocouple had gone bad, but the problem seems to be in the timer itself. There are only two controls on the dryer - the timer knob and a separate start button. To use the dryer, you turn the knob to, say, 40 minutes of dry time, press the start button, and the knob will still slowly revolve until it gets to 0 and the dryer stops. When the knob reached 5, you'd hear a click and the heating element would turn off. The timer will turn and count down even if you don't actually start the dryer, and it still stops at 5 minutes left, right after you hear the click. There are two cycles on the knob (regular and low-heat, each taking up about half the knob) and it stops at 5 minutes left on either cycle.
Any ideas on how to fix this? Do I need a replacement timer (or some other part), or is it likely there's a DIY fix for this if I'm willing to open the dryer up that doesn't involve buying a new part?
The dryer model number is DDP1000NATWH, I'm guessing about 30 years old. It's a *very* small dryer, about 21" wide and deep, 120V, non-vented. There's nothing like it available new (except really tiny Asian dryers with much smaller capacity); I've only seen one other like it at a used-appliance store. The appliance-parts sites I checked don't recognize this model number.