Linkage Adjustment for Neutral Safety Switch?

My 1967 Dart with a 727 Torqueflite will engage the starter in neutral, but not in park. Once in awhile it will engage in park, usually after the car is warmed up. The engine has been pulled twice in the last year. Can anyone give me a simple explanation on how to adjust the linkage to alleviate this problem? Thanks!

Unless you have pivot points in the linkage that are too sloppy you should be able to put the selector in park and loosen the adjustment point in the rod and then retighten it.
This can allow the linkage inside the trans to center on the park position.
Of course there are possible reasons other than this (like a worn switch) but it works a lot of the time.