Hard to determine the fix until the problem is diagnosed. I would suggest having someone check for codes, and go from there. It could be something as simple as a blown fuse, so you might want to start by checking the fuses, and then go from there.
Your local AutoZone(if you have one) should be able to scan it, and give you a print out of any codes.

btw...most places like AutoZone will do the code check for free...

Hem, this might be a long- shot, but you never know.

Got any pictures of your 93 HKW????  I would love to see your vette!!

This is a common problem on 1990. Check for code(s). Go to terminal under drivers side dash on right side. I like to ground on the driver seat and connect other end to Terminal "K"..2nd row 3rd from right. The Rest. lite will blink code 12 (1long-2 short) 3 times..after this the default codes will start blinking ..3 times for each default(s) and then finish with 3 times for code 12 again. Most likely you will see a code 26 as this is the majority of problems. This represents the air bag sensor on the passenger side. Disconnect the battery ..and now the fun begins. You have to take off the side fender and possibly the inner fender to get at the sensor under the rad. reservoir. There are 2 bolts holding it down(tight and cramp spacing). When off; sand the frame area and the underside of the sensor well to remove any corrosion if any and apply dielectric grease to the surfaces. (***this was GM's fix to this problem for 1991). Reassemble and connect battery. Now comes more fun....to clear code(s) for Rest. lite AND seat belt lite...turn ignition on but not to turn over engine.....connect to K terminal  and ground(seat)..wait for the 3-12 code flashes then start this clear process....unground for 3 sec...ground for 3 sec....unground for 3 sec. and ground for 3 sec....unground for 3 sec. and ground for 3 sec...UNGROUND for 10 sec. and turn key off. It IS IMPORTANT that your timing is EXACT..you only have a +/- 1/2 sec. window of tolerance or you may be doing this proceedure over many times.

[QUOTE=UNCLEBILL]This is a common problem on 1990. Check for code(s). Go to terminal under drivers side dash on right side. I like to ground on the driver seat and connect other end to Terminal "K"..2nd row 3rd from right. The Rest. lite will blink code 12 (1long-2 short) 3 times..after this the default codes will start blinking ..3 times for each default(s) and then finish with 3 times for code 12 again. Most likely you will see a code 26 as this is the majority of problems. This represents the air bag sensor on the passenger side. Disconnect the battery ..and now the fun begins. You have to take off the side fender and possibly the inner fender to get at the sensor under the rad. reservoir. There are 2 bolts holding it down(tight and cramp spacing). When off; sand the frame area and the underside of the sensor well to remove any corrosion if any and apply dielectric grease to the surfaces. (***this was GM's fix to this problem for 1991). Reassemble and connect battery. Now comes more fun....to clear code(s) for Rest. lite AND seat belt lite...turn ignition on but not to turn over engine.....connect to K terminal  and ground(seat)..wait for the 3-12 code flashes then start this clear process....unground for 3 sec...ground for 3 sec....unground for 3 sec. and ground for 3 sec....unground for 3 sec. and ground for 3 sec...UNGROUND for 10 sec. and turn key off. It IS IMPORTANT that your timing is EXACT..you only have a +/- 1/2 sec. window of tolerance or you may be doing this proceedure over many times. [/QUOTE]

sure is a lot of checking. mine stays on too. there are a couple problems with this. 1990 only had a drivers side airbag unless passenger side was a special order. i have 2 scanners and neither show a t/c. PO said it happenned to him and he had the sensor replaced even though gm said there was nothing wrong with it at a cost of about $600 (saw the receipt). maybe the diselectric grease is the answer even in 1990s.

[QUOTE=eddie20890] [QUOTE=UNCLEBILL]This is a common problem on 1990. Check for code(s). Go to terminal under drivers side dash on right side. I like to ground on the driver seat and connect other end to Terminal "K"..2nd row 3rd from right. The Rest. lite will blink code 12 (1long-2 short) 3 times..after this the default codes will start blinking ..3 times for each default(s) and then finish with 3 times for code 12 again. Most likely you will see a code 26 as this is the majority of problems. This represents the air bag sensor on the passenger side. Disconnect the battery ..and now the fun begins. You have to take off the side fender and possibly the inner fender to get at the sensor under the rad. reservoir. There are 2 bolts holding it down(tight and cramp spacing). When off; sand the frame area and the underside of the sensor well to remove any corrosion if any and apply dielectric grease to the surfaces. (***this was GM's fix to this problem for 1991). Reassemble and connect battery. Now comes more fun....to clear code(s) for Rest. lite AND seat belt lite...turn ignition on but not to turn over engine.....connect to K terminal  and ground(seat)..wait for the 3-12 code flashes then start this clear process....unground for 3 sec...ground for 3 sec....unground for 3 sec. and ground for 3 sec....unground for 3 sec. and ground for 3 sec...UNGROUND for 10 sec. and turn key off. It IS IMPORTANT that your timing is EXACT..you only have a +/- 1/2 sec. window of tolerance or you may be doing this proceedure over many times. [/QUOTE]

sure is a lot of checking. mine stays on too. there are a couple problems with this. 1990 only had a drivers side airbag unless passenger side was a special order. i have 2 scanners and neither show a t/c. PO said it happenned to him and he had the sensor replaced even though gm said there was nothing wrong with it at a cost of about $600 (saw the receipt). maybe the diselectric grease is the answer even in 1990s.
[/QUOTE]      

well unclebill was sure right on this one--- it is a real pain. last weekend i took the sensor on the drivers side and cleaned the frame and sensor and reinstalled using the diselectric grease. as the book from the body shop showed there was only one i figured i was done. WRONG. lite stayed on and after a little reading of a set of jumper plugs that i bought from ecklers learned how to read the codes in that computer.

sure enough it showed the code for a right side sensor. so much for the book from the body shop. i have been working on the 75 so later this afternoon i did a couple of things to the 90. i thought that maybe the code had to be cleared manually so i printed out unclebills directions for clearing the code. sure wasn't that much fun as it took me about 4 tries and ta-da both lites went out. i was hoping that i would not have to mess with the right side.

had to run to the store so i jumped in the 90 and was waiting for a light to turn green and looked down and lites were back on. . looks like i will be taking the right side off probably next weekend.