Dart 63 shift cable

I assume 1963 and 1964 would be the same, so no the park cable is not going to have anything to do with reverse. The park lever being lifted will release a cable that holds the parking gear on the output shaft of the trans with the park sprag. There is a separate cable that controls the gear selection when the buttons are pushed. If the car starts when the park lever is down or the car is in neutral, I wouldn’t think your gear selector cable is stretched. If you have to fiddle with the buttons to get the car to start then I would think you need to adjust the gear selector cable. The field service manual has a couple of paragraphs detailing this process and I can snap pics of it if you would like. Doug.