I'm not familiar with your model and I'm wondering if it's actually a timer that's gone so when you put it to a 'power' setting it's actually the length of time the grill is on, a bit like a dualit toaster.
Thermostats control temperature only and don't normally turn off but control the temperature, timers control time I'm betting it's a mechanical timer that's siezed up .....WD40 ! Model and serial no ......I can bring up a exploded diagram with that info .
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