It's not hard to imagine that there is no good reason to have a neutral safety
switch on a car that uses the neutral button as the starter switch. Think about
it. There is, however, a vacuum switch on the intake manifold that prevents
the starter from engaging if the engine is running. It's just so much less
commotion when you hit neutral to park the car. If the vacuum switch isn't
happy, you'll have trouble starting the car. Replace it, and all should be
well.
Cheers,
Roger