It's pretty easy to see why this switch wouldn't work at all. The center dimple is completely green from corrosion.

This is the contact after sanding off all the oxide with some 400 grit paper. Make sure that you also do the rim as the spring contacts it there and it part of the switch.

Lightly sand both ends of the spring so that you have bright metal.

The other contact surface must be cleaned also as it's also covered in oxide.

This is the contact after cleaning. Make sure to clean the area around the contact as that is where the spring touches and it's part of the switch.

Sand any oxide off where the wire ring touches the contact plate. Put a dab of dielectric grease on all the contact points in the switch and reassemble. The tab on the contact plate goes under the button pivot pin as shown by the arrow.