My vote is for the ignition switch or security system.

Had something like this is a Ford. Turned out to be a mercury roll over switch that shuts off the fuel in a roll over accident. Switch was about 9 bucks, took me months and 5 tows to the shop before a new service manager knew what it was.

Also same car, battery had a broken terminal inside the battery. Would run just fine, then get somewhere and wouldn't start. Was a real off and on thing. Might swap out the battery for a little bit to see if anything changes.

I would assume that when he says all the things that are "good" they have all been tested/replaced.

Did you trouble shoot all the fuses, relay, and ignition switch? Here's a wiring diagram.

http://www.ricksfreeautorepairadvice...dodge-plymouth

New battery, new starter. The odd symptom is that when I crank the key and it doesn't start, it clicks the accessory relay.

When it starts, the starter relay clicks. I have taken it out on a drive the last few starts with the same result, it runs and drives fine, I bring it back home, shut it off, then start it again, then shut it off, and start it up again, rinse, lather, repeat about 1/2 dozen times. I let it sit for a few minutes and it's not starting when I turn the key, just clicking at the accessory relay when the key is turned to the start position. It usually won't start after that for at least 12 hours.

I'm in that process, the starter relay pin 85 has continuity to ECM pin 30 so we're good there, also there is continuity between pin 87 and the wire to the starter, the big hot wire is hot.

It's a base model, no anti theft.

I'm getting a 11.66 volt reading on my ghetto multi meter at the ignition switch in the key on position, it's reading 0 with in the off position. Does that rule out the ignition switch?

Not necessarily. You will need to verify you are getting battery voltage with the key in the start position. Looks like it goes directly from the switch to the starter relay so you could test it at the relay terminal.

It turned out to be the CPU.

I threw a lot of time and parts at it trying to figure this out, but that's what it was.

I sold it and bought a 2015 Ram Sport, I love the 5.7 Hemi, such a fun truck to drive.