Aha - a 555 chip, a transistor AND a capacitor - just as I thought ;P
That's not a bad start thanks Neil, but from what I can tell, it's push on/push off. It's not triggered by the car feed. It's a good fallback, and I might just try it, but I'm looking for something slightly more automatic really.
Re: your comment about the resetting - it's a good point, I hadn't thought of that, but as far as I know, our DVDs don't do that if going from Key to start is any indication. I'm pretty sure the permanent power feed is, well, permanent

and reliable. The power doesn't seem to drop or spike in any significant way that affects this. I guess if it did, all kinds of things would get reset eg. Nav.
This could be a factor of the larger battery on Nav setups?
Still hoping for a closer solution...