Another laundry-related timer problem

Got a Kenmore washer, probably going on 20 years old, works fine. But it has developed an annoying glitch: after the wash cycle is over, it doesn't turn off completely. There's a *faint* buzzing sound that persists (solenoid energized???) until you push in the timer dial to shut it off. Nothing runs, no motor, no water flowing, just a quiet humming sound.
Anyone familiar enough with these beasts to suggest remedies? Squirt some contact cleaner in there somewhere?
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Mechanical timer? Most are powered by a tiny synchron motor and it may just be losing its strength. Bearings, tight spot on the gears, lack of lube. I'd hit it with contact cleaner and maybe some silicone spray to lube it.
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