This exactly. First thing which has nothing to do with your problem is look over the shift linkage and ADJUSTMENT which is usually under the car. Maybe it's the shifter and maybe a bad bushing which you can fix. Or maybe it just needs adjusted
Next, with the thing cranking, pull either "push on" wire off the start relay. If it quits, it's being powerd in that circuit. If not, might be sticky starter relay, wiring problems down to the starter, or in the starter / solenoid itself
