A timer that advances through off is completing the timer motor
circuit either within the timer or at another point within the
machine. You will need to look at the wiring diagram and see which
contacts within the timer open to cut power to the timer motor when
the dial reaches off. Then with the machine unplugged, remove the
wires from those contacts (if they come off) and do an ohm test to see
if the contacts inside the timer are really open. If they are, then
the timer motor is getting power through a back door and you'll need
to figure out how. Since the timer motor isn't 240v, it is a bit
unusual that it could have contacts that are stuck closed, but I guess
it is possible.