I have to wonder if the mechanism is a little sticky and every once in a while it "breaks loose" and runs for a bit. I've had music boxes do that. Did you open it up and play with it to see if it's sticking? Even if it doesn't seem to stick when you wind it up to play it, it might be a little sticky and it'll stop before the spring has fully unwound, and then it might, at some random time later on, start playing again (temperature changes often cause this).
If you open up the box so you can get to the mechanism, try to work it so the spring is fully unwound. Or give it a quick spritz of silicone spray or WD-40. Once you've fixed the stickiness, or confirmed that it's fully unwound, put it back together, and see if it still plays without winding it. If it does, it could be paranormal in nature.
(Time to add Music Box Fixer to my sig line)
![[Rainbow Smiley]](graemlins/color.gif)