The Instrument Cluster lights are on, but the Dimmer Switch is off.

Regardless of the Dimmer Switches positon, the Console lights remain off.

This all started when I went to turn on my Fog lights one night, lights started flickering for a few days and finally went out.

 

XJ-8 interior lights are switched on and off by the BPM or more to the point a transistor inside the BPM.
This particular component provides the dimming of the lights and will eventually shut down the interior
illumination. It is unlikely that the switch is bad as they don't get used a lot, and is more likely the BPM
has gone south or maybe just the switch itself

 

Out of curiosity, how long have you had the car?...do you know of any previous dash work done to it? I suspect a possible umbilical or other connector not being totally seated or scarred is why I ask.
It easily could be what Randy describes as well.
I attached a PDF for review.