I would expect that the timer thing itself needs power - and will have power going through certain contacts when the system is supposed to run. Can you check for 110vac (?) through the timer when you press the button ?

Also, I think that there is a relay that turns the motor on and off, check for voltage on that when you press the start button.

if the timer doesn't run on 220v, then there should be a small transformer somewhere, see if that is putting out 110v when needed.

-John

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