I am not a brick expert but I have '90 model with same engine and my ABS light will stay on if I do not slightly turn my ignition key back after starting. I think my spring is busted or something. I would try wiggling your ingnition switch a little to see if that takes care of your problem. It not I would start checking out your sensors at the wheel callipers to see if there is too much build up on the magnets or to much build up on the splines.
Then I would check my brake fluid to see if it is too dirty, especially on the bottom of the brake fluid reservoir. If so then flush system. Check FAQ on this website and it will walk you through the steps.