From the sounds of this, I would guess you have a Gennie Shifter with the integrated neutral safety switch. These are prone to corrosion as you have apparently found. They are also prone to failure over time. You might want to clean it, simply spray contact cleaner on the switch, or replace it. All are simple fixes once you crawl under to reach it. And once cleaned and adjusted, they offer invaluable protection! (this should only take 10-20 minutes)

As for the advice you are getting about keeping the NS switch, this is some of the best advice you'll get for free. Too many times, cars are started when the owner "knew" the car was in park. Nevertheless, the car jumped out of nowhere and the damage was done before it could be stopped.

These hot rods (and our family & friends who are standing near the cars) are too important to take the unecessary risk. You are making the right call by keeping the NS switch.

This site is really cool. I remember wondering the same "Am I going to hurt this if I disconnect it?" question many years ago. I only wish I could have had a resource like ClubHotrod to seek out the help back then like we do now.