So you're saying that the warning lights in the instrument cluster work, but the nighttime panel illumination does not?
Does the panel illumination work on the HVAC panel? I think on your car the 3 HVAC dials and the buttons underneath should light up in green when the lights are on.
If the lights on the instrument panel don't work but the one's on the HVAC panel do, I'd check the light bulbs at the back of the cluster.
If all of them don't work, I'd look at the light switch. On my Mk1 the rheostat that controls the panel dimming function has some dead spots where the lights go out, and I have to make sure to adjust the dial carefully to avoid them. If the panel lights flicker as you slowly move the dimmer dial while the headlights are switched on, you might have the same problem.
Have you tried swapping in a known working light switch from someone else's car (assuming you have access to one)? Should take <5 minutes to do, and will give you a good idea of where the issue lies. I think any Jetta or Golf of the same vintage should also work, but I'm not sure.
The Bentley manual might also have a wiring diagram you can use to figure out how to test your switch with a multimeter. I don't have my Bentley in front of me, but I assume it has some sort of info on what the different pins on the back of the light switch go to.
Also, a stupid question, but have you checked the fuses already?
Finally, if power is getting to the light switch in the right places, and the light switch is passing power through to the correct pin for the panel lights, you'll have to check the wire going from that pin and see if there is a break in the circuit somewhere. I'm not sure if the instrument panel illumination has it's own ground separate from the warning lights, but if it does, that would be something to check as well.