I had a problem with the Instrument cluster illumination in my 1992 XJ40. It stayed always on, only way to switch it off was to disconnect the battery.
I found out that the problem was a shorted transistor on the PCB, it is marked as TR3 on the board.
The transistor type is a ZTX751. Bought a new one from Mouser Electronics for less than a dollar.
Replaced it and the unit now works as it should.
Hope this can be of some help for others with the same issue.