58 Imperial does not have a neutral safety switch. What it has is a neutral
starter switch. The neutral button is the starter button. The key does not
activate the starter, it just opens the electrical circuit.
I cannot say what is causing the problem's on this particular 58. There are
a variety of answers, any one of which might be correct. When it happened
to my 58, it was the coil, but it could just as easily be a bad connection
or a starter motor problem. There is also a ballast resistor to be looked
at as well.
What the car needs is a mechanic to diagnose the problem. It will get worse
and it won't always fail to start in a convenient place. Replacing the coil
worked for me, but I chose to replace the ballast resistor and get the
starter motor rebuilt not too very long after. I went from taking five
attempts to getting the 58 going to it starting on the first try.
Hugh
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