I have had an interest in this topic also for my 04 RS which does not have an illuminated key ring. In the last exchange I had on this topic I noticed that there was no existing wiring (this would apply to an 02 also). This was based on comparing the wiring diagram for an 04RS to the STI. Another poster argued that the wiring to make it illuminate and dim was a function of the ring itself. He said he was going to buy the ring and the two pieces of plastic above and below the ring (requires a larger opening than the existing stock plastic). I never heard back from the poster, although I may have missed some additional post.
If I was going to try this I would purchase the ring and the two pieces of plastic above and below it. Then I would assume I would have to power it independently from the dome light. I would use the positive brake light for a source of power since it is available when the car is off. Get in the car push on the brake and it would illunintae.This theory depends on whether the bulb can be powered by a 12 volt source. Yes the light would come on whenever you pushed the brake but so what.
So to answer your question no ones knows as far as I can tell.