There'* a few guys that have this problem--not many tho.
I've jiggled wires throughout the engine bay and under that dash--beat the **** out of my dash--w/no results! If you look behind the glove box you'll see some more fuses and relays--one spot is marked DIC w/a fuse--check for power. Once I was lucky enough to have my compass come on-so I pulled over and tested that DIC fuse for power--no power but the display was on--weird!!
BTW--have you checked your lcd'*(screens)? Do they still work?

Check the body control moduele.

Where would that be and what does it look like?
Does it control the info screens?

>> I'm having the exact same problem w/my 89
>
> Same thing with my 88...

My '93 does it sometimes as well. It'* grubby edge connectors, I think. I can fix mine for a period of time by thumping on the left end of the dash, kind of just below and inboard of the left-side dash air vent. Requires a weird turn of the wrist to thump on it while you're driving, but when you hit the right spot, both displays pop back to life. Sometimes some of the components don't light up right so more thumping is needed. Problem is worst on cold days, I find, but goes away by itself once the car gets heated up inside.

-- Andy

I've tried kicking, banging, twisting, sweet talking, cursing, pleading--you name it, I've tried it! no such luck! Must be a female SSE!! :P