Often the problem can be easily fixed by using a thinner sealing washer. Here I used a diff drain/fill plug washer (right). It isn’t a solid washer, and crushes thinner than the original washer (left).
But first, make sure the switch functions properly by performing an ohm check while depressing the switch (requires removal of the switch). The switch shouldn’t need to be pressed very far to close. If your switch is bad, a new one can be found at your local Toyota dealer, part number 84222-12010.