Interesting thread! I have an old Fluke 8020A and 8022A, which both still work EXCEPT that the 8022A has a couple of the decimal points on the LCD permanently on. I've tried disassembling it, cleaning the LCD edge, the zebra strip and the PCB, reversing the zebra strip, visually checking for any board shorts, etc, but no luck. Without the circuit I couldn't think of anything more to do, and decided it was probably a fault in the main chip anyway.
So, the schematics are available! Cool. Time to have another go at it.
I don't suppose anyone else has ever had this problem, and fixed it? See pic.
Edit: FWIW, I recall hearing long ago that sunlight was bad for LCDs, so I always avoided leaving these meters in sunlight. This might be why their LCDs are both still perfectly good.
Maybe this doesn't apply to modern LCDs?
Edit2: Dammit. All the amazing 'restoration of old test gear' threads here - cannot unsee. Now I feel guilty every time I look at some of my old gear and realize it could do with cleaning.