Power media device from dvd player?

We've got a 2007 Sienna with an after market roof-mounted dvd player. It has a/v inputs and we've been using our western digital media device in it using a power inverter via the cigarette lighter. But I'd really like to cut down know the cable clutter. So I'd like to see if it's possible to power the western digital right off the same power the dvd player is running off of. Which is basically the power for the dome light that was there before the dvd player. I haven't broken out the multi meter yet to see what power is running through there. (I'm assuming 12 volts?) Anyway, what would have to be done to power the media player off that same roof power? I mean like literally bastardizing the ac adapter and hard wiring the power cable to the dome light power. The ac adapter output is 12 volts, 1.5A, input is rated for 100-240v, 50-60hz, .5A max? I would love it if I could tie it right in to the power lines but Iknow tthat's probably a pipe dream. Any thoughts?

Btw, I plan on sticking the media player to the lid of the dvd player with velcro or something. This way it would be all contained with no wires hanging down.

Bump

Just took the DVD player down to measure the voltage coming from the power cables for the dome light that is powering the DVD player. About 9 volts. is that right? My media player requires 12 volts. Is this going to work?

I've thought about scouring ebay to find a broken roof mount DVD player where maybe the disc drive or something is broken but the screen still works. Then tearing the sucker open and hard wiring the guts of the media player right into the case of the DVD player. But I definitely do not have the elctronics background to do that.