Not sure how long it's been going on, but when the car is parked and off, the instrument cluster lights up for about five seconds, then goes off for a couple seconds, then lights up again, repeatedly. The start button also lights up with it. I've tried to eliminate several causes:

• I had wired an aftermarket backup camera to the reverse lights, but yesterday I undid all of it and it is still happening.
• I replaced the battery (it was 6 years old) as I've heard a dying battery can cause weird stuff like this.
• I pulled both ignition relays to see if it would stop the problem, pointing to something with the start button - no change.
• I changed the battery in the keyfob just for kicks, but this happens even when the key is nowhere near the car.
• It does not seem to be the open door sensor, because the interior lights don't come on - just the cluster and start button.

The next few things I (or the internet) can think of to change are either time-consuming or costly:

• Replace the start button
• Replace the cluster
• Flash or replace the PCM

BTW, this does not seem to be causing ANY PROBLEMS! The battery is not dying, the car has sat over 24 at a time without being started while this was occuring, and the car still always started right up, even with the old battery. That's why it's tough to decide to spend too much time or money trying to trace it down. I just don't like it when something's not right with my wife's car.
2012 Journey SXT 3.6

Any experience or further troubleshooting ideas would be welcomed.

 

Mystery solved! It was the bluetooth OBD scanner that I leave plugged in. It never drew enough power to kill the battery, but is just weird. When the OBD scanner is unplugged, the problem goes away.