Chris & Ted,
I'll look in my GM Shop Manual later and get back to you two. Right now I'm having one heck of a battle with my computer. The desk top died, so I'm using my laptop and it keeps kicking off line
I would check the switches at the door. I would start with the switch on the driver's side, It is the switch with 2 wires conncted to it the one on the pasenger's side only has one wire attached.............Steve
Steve (SSAutoSport) suggestion is a very good place to get started. Should these prove to be ok, then Check the ground from the vanity mirror make sure it is a good connection. The common circuit to these lights is the Light Delay Timer check it's ground too, the grounds are the black wire.
I am assuming that your instrument lights and cigarette lighter are working? If it is only the interior lights associated with the door switches, and the ground have been cleaned and check as mentioned above, you could try to bypass the Light Delay Timer and see if the light work then.
The Transistorized (black box) "Interior Light DelayTimer" is located under the dash between the glove box and the side panel. Maybe just cleaning all the contact surfaces will fix you up, but you may need to replace the Magic Little Black Box.
Hope this is something simple, Like ground connections or bad bulbs, does your walk around light work on the back under the Corvette?
Good Luck and keep us posted as to what you find, I'm sure others have the same problem and watching too