Q: Starter turns over whenever I shift over Park or Neutral, intermittent problem.

This problem is intermittent and I am at my wits end trying to diagnose the problem. On occasion when I start my truck up and drive somewhere, I'll come to a stop and shift into park and the starter will turn over. I don't hear any grinding as though the solenoid engaged, but all the lights dim for a second due to the draw from the starter. Shop said it was the neutral safety-switch, I replaced it, problem didn't go away, got a refund for the shotty diagnostic job. I have replaced ALL Relays, fuses, and breakers, on top of the starter itself, the ignition switch, and the neutral safety-switch. Another thing to note is that on occasion when I disconnect the battery and reconnect it, the starter will turn over and I was once able to start the truck this way in spite of the fact that the key wasn't in the ignition. Recently my AC module has occasionally stopped working and restarting the truck will fix it. Also there has been a random clicking from behind the dash

My car has 185000 miles.
My car has an automatic transmission.