1965 Dodge Dart GT will start in neutral but only sometimes in park

Unlikely to be the switch because it always starts in neutral.

Not true, I had an aftermarket one fail like that in the Duster. If I slammed it into Park on the times it failed to start in Park it would usually work after that. The rooster comb that pushes the switch is not exactly the same profile in Park as it is in Neutral so it may be on the edge of not working in Neutral and over the edge in Park due to that difference. I now only use new old stock switches.