i have a similar problem, 93 s13 vert, auto-manual swap, rb20det swap.
i pulled the motor out of my old vert (94) and put it in the new one, my old vert didnt have this problem so im thinking its something particular to the chassis. ive tried 3 different column light switches, dash and tails stay on as well as sidemarkers, when i turn 1 click for parking/sidemarkers the dash gets brighter. The other problem is, it may be unrelated but my headlights dont go down, the button will make them go up, turning the lights on make them go up, but they will not go down.

halp