GMC53,
I am not familiar with this light switch. A conventional wire wound rheostat has the wire embedded in a ceramic housing and a shaft of some sort with a wiper attached. The surface between wiper and wound wire becomes scaled and cruddy. Sometimes the heat generated by the wire itself will destroy the tension in the spring that holds the wiper against the wire.
Cleaning the mating surfaces with some fine sandpaper can often restore the connection. Put a little piece of 320 grit paper under the wiper and run it through the range a few times. Make sure the wiper pushes against the wire.
If this isn't how your switch is constructed, disregard this blurb.
Stuart
