It could be the neutral safety switch, sometimes the contacts get burnt and messing with it scrapes away enough of the burnt stuff to where it will make a good connection.

Problem is you have a newer vehicle. Your neutral safety switch is not as simple as the earlier switches, it also has a bunch of wires that tells the computer what gear you have selected.

Go down on the side of the tranny and see if you can find the switch. When you find it, look for a darkblue/orange wire and a tan/red. The darkblue/orange comes from fuse 21 which is fed by the ignition switch, and the tan/red goes and feeds the starter motor terminal. If you could somehow jump these wires out, you could see if the problem went away and verify it is the switch. Just be careful if you do this, it will start in gear.