2006 X5 3.0i keeps running with key off

[Siggy]

2006 3.0 with 156,000 miles on it. Saw some odd behavior about a year or so ago. Alarm would go off at night time, but only after driving it for a couple of hours. Thought it was the battery going low so I replaced the battery and all seemed well for a little bit. Then it would go off, I'd go outside, all the lights would be on, the AC fan blower motor would be on, blowing air out the vents, all the lights lit up, engine failsafe warning. No matter what I tried, I couldn't make the lights go off. I'd start it up, drive it to work, drop it off, and it would shut off fine. I don't think it happened again during the night because it always started the next day.

Finally replaced the ignition switch about 6 months ago. Seemed to solve the problem. Didn't have any more quirky behavior.

Now, it's back. Drive it for 1 hour, and that night, the alarm will go off and everything will be on. Some times when you take the key out and get out, the outside cooling fan will run for about 20 seconds and then cut off, even if it's cold outside. A couple days ago, I got in it, turned the key and all the locks cycled to unlock all at the same time and the car didn't start. I turned it off and back on again and it started.

Put another ignition switch in it tonight, buttoned it back up, started it, it started right up. Turned the key off and it kept running. Pulled the key out and it kept running. Clearly I'm missing something here.

It's a good, newer battery (less than a year old), new alternator, 2 new ignition switches.