John,
The notorious 'previous owners' do strange things sometimes. The mystery switch would certainly merit further investigation though.
If it is a momentary switch, it couldn't replace the key switch. You have looked at the starter and it doesn't have a solenoid..right.
This rig has a standard transmission in it I assume. The Hydramatic rigs used a solenoid actuated starter with the pushbutton on the left of the steering wheel, mid dash. They wouldn't have a stomper though.
Stuart
