The Ford N series DID indeed have safety interlocked start buttons.. ( 2 types ) the very earlies 9n did not have this feature. The later 9n and all 2n had a mechanical linkage / tranny neutral interlocked switch that activated a large hi-current switch between the battery and the starter. I fthe shifter was not in neutral, the starter button could not be pressed enough to move the mechanical linkage to press the big starter switch at the front of the steering column.. The 8n , naa, and hundred series used a grounding tranny neutral interlocked switch.. the switch merely provided ground for the 'internally hot' 3 wire oem solenoid. thus completing the circuit. if the shifter was not in neutral, the button could not be pressed far enough to complete the circuit.
If jiggling the shifter made the start button work, My guess is a worn shifter pattern on the underside of the tranny shifter cover.. that is also where the big thumb interlocked button is attached with a locking tab and retainer.. The shifter pattern gets so much wear thatt he interlock plate is not moving sufficiently to unlock the start button.
Some have had luck with brazing the worn points up.. other repalce with working salvage.
To test the solenoid and starter, you can remove the single wire from the base of the switch. if this wire is then touched to frame (ground ).. it should allow the solenoid to energize.. so make sure you are in neutral before defeating this safety interlock feature that ford had in place since the late 30's
An ohm meter can then be used on the thumb switch.. you may be able to shif the tranny almost in or out of a gear and get the switch to work, thus confirming the worn interlock shift pattern.
The I&T FO-4 manual has diagrams and pictures of this part.
If you do remove the shifter cover.. do so slowly.. there is a single spring and detent ball that will be held under a little pressure.. make sure you lift slowly and capture the parts and don't let them fly off intot he shop or into the xmission..
Also.. as a note to Bill.. the ford oem 3 terminal solenoid alread has one side of the coil tied to the incoming starter wire thus making it internall hot.. therefore shorting the hot line fromthe battery to the small 3rd line does absolutely nothing..you would be applying power to both sides of the solenoid coil... that small 3rd terminal needs -ground-
Sundguy