We have a 2008 IC with a 365, and it will sometimes run after the key is turned off. Generally it will run for about 5-10 minutes and just shut off, but last night the driver said it ran for about 3 or 4 hours before shutting off!
The key switch is new. The mechanics are thinking it's something related to the programming.
I've got one that's about that same vintage that the dome lights will come on and stay one part of the night. Haven't had that trouble this school year. Don't know what the deal was. I wish it would burn down! Not with kids on it of course.