I'm having a similar problem (06 Lariat Screw 4X4) but not as severe as many in this thread. My stereo stays on (and never goes off) with key out and door open. However, I'm not experiencing any of the other issues discussed. Door ajar light & chime works with every door, windows don't have power after door is opened, nor does the sunroof. The dome light comes on for a few minutes with any door opened (closed).
This seems isolated to the stereo (and clock).
I inspected the violet splice as described and it has an appropriate shrinkwrap seal, not hockey tape (previuos repair maybe??). The lower channel did have water but I have found no corrosion in any wire.
Odd thing, my stereo was off when I parked two days ago (went off when I opened the door). I went out to the driveway this AM and heard it playing. Daughter said it wasn't on when she went to school at 07:30 but at 10:30 (when I went out), it was on. So, it turned on by itself sometime between 7:30 and 10:30. It was raining two days ago but not yesterday or today.