While I haven't looked in this are, it probably would be pretty simple. The light doesn't use a switch, it's either always on (with accessories), or part of a light circuit.
Instead of spending money on incandescent lights, like Honda did, I think you could get better results, quite possibly cheaper, by using LEDs. A couple of white or yellow (or red or green, if you're feeling more creative or Christmassy (Christmassy?, you get the idea)) LEDs should do the job nicely, draw only about 20ma (up to about 6 of 'em can be wired in series without drawing any additional current), and produce virtually no heat. And, the LED's will never burnout.
One easy way to mount them would be to simply drill holes in the back top edge of the compartment, near the top and push the LEDs in from the backside with a force fit. A "drop" of glue should make the installation permanent.
I'm planning a similar installation in the glove compartment but with the LEDs mounted on a bracket above the latch.
Mel