I'm going from fuzzy memory here, so double check what I'm saying. There is a remote dimmer module somewhere under the dash, AC Delco p/n D1509B. It is a transistor circuit that controls dash illumination when the lights are on. I believe (again, double check me here) that when it fails the dash lights work only when the headlight switch is off. The factory service manual has the complete troubleshooting sequence I think. Note that this module is NOT the dimmer switch-- it is separate. Rockauto has them for about $30. They're used on a bunch of GM vehicles from mid-80s on up, so you can probably find one in the boneyard if you want a cheap one as a "try-and-see" part.