HappyAdventure

I have an intermittent issue in a 2004 Tacoma with an automatic transmission where the starter will crank on it's own without the key being turned to start, sometimes without the key in the ignition at all.

Initially I thought it may be the starter solenoid getting stuck, so replaced the starter contacts.
The problem came back, and even had a couple times it started cranking while parked. I tried replacing the starter relay.
Zombie starter kept randomly cranking on its own, so I replaced the ignition switch.
Then the entire starter.

Sometimes it will start cranking when I put it into park.
Sometimes it will start cranking when I just put the key in.
It will usually stop if I shift to drive, but not always.
It will stop if I pull the starter relay.

So maybe a short somewhere between the ignition switch and the relay? Any suggestions on tracking down an intermittent electrical problem? Parts seem to test ok when it is not in zombie mode cranking on its own, and I can't really test while it is just sitting there cranking.

I have looked for a remote start kit, and not found anything.

Edit: Attached is the wiring diagram.