The first thing to do is place the car in a dark garage. If you don't have a garage, place a book on the top center of the dash. There are small slots sort of near the windshield, be sure they are covered. The car has a photo cell that control the panel lights.

Once that is done, turn your key "on" and press the fog light switch. Do not turn on headlight switch. Does your CRT and Speedometer dim? If not, move the slide switch under the headlight "off" button back and forth. Does the CRT and Speedometer dim now? If the answer is yes to either question, the problem is the headlight switch. There is a cure that works most of the time. Note I said most of the time, sometimes the switch does have to be replaced. Get a can of WD40, some state that contact cleaner should be used but many such compounds damage the plastic. Make sure the WD40 can has the little spray tube. With the spray tube inserted between the slots in the switch, spray a very small amount of WD40 while pressing the buttons off and on. Do this on all the buttons on the headlight pod. That should fix your problem.

If your CRT and Speedometer did not dim when turning on your fog lights, then the photo cell may be shot. [The reading in the BCM data for photocell must read 74 or more to put car into night mode.]

Check the operation of the dimming pot and the photocell by  using the Reatta onboard diagnostics screen. Accessing BCM input BD42 gives the value of the dimming pot (0 min, 100 max), BD44 gives the reported reading of the daylight sensor (close to 0 - daylight, close to 100 -night). BS03 can override, the dimming value. (See section 8D of the FSM for more information.)

There are two (2) 110 volt inverters some of the instrument lights.  One for the dash and the other for the transmission display, (that item, in many cases, is bad) the power window, and mirror control. A good test for the inverters is: they are working if when the "light show" (lifting up on drivers outside door handle) occurs, all of the switches light up.

If only the speedometer, warning lamps and CRT light up and the switches do not, then the inverters could be at fault. I may be mistaken, but I don't think the inverters have anything to do with the dimming circuit of the speedometer and CRT when the headlights/fog lights are activated. As I understand it, the inverters supply 110 volts for the VFD's that provide light to the switches. The console mounted fog light and manual headlight control switches on the '88 & '89 have bulbs. That is also the case with the buttons below the warning light display.