Going on the pics you sent, I would suggest that when the unit was assembled and the switch was off that the white pin would have been held in a "pushed out" position by the stalk such that the contact spring strip on the back of the switch casing is held open.
When the stalk is then twisted, there must be some sort of cam in the body behind the white pin that moves inwards and so taking the pressure off the contact spring strip allowing the contact to be made. This will sent power or and earth to those 3 long spring strips inside the switch body.
So, this being the case then the white pin should be allowed to move inwards when the stalk is twisted to the on position.
Have you cleaned the connection for the spring strip on the outside of the switch body ? Maybe even test to make sure a conection is made in its current disassembled state.
Cheers,
Steve