the radio has two power sources, one thats keyed, and one thats an always on. if you've ever put in a cd player the red wire I believe is the power that comes on with the key, the yellow one is the one that provides power all the time. I'm not sure what color the wires are for going into the back of the stereo, but I'm thinking you could run it off of there if you had your heart set on using the same power thats going to the stereo, though in the long run I would just follow a different process mentioned above. I might even wire it into its own block on the fuse box and use a mini fuse. but its up to you, there are probably a dozen different ways to wire up the dome light so it will work, so its not as though if one doesn't work out the best, you don't have more options.
good luck