Well 5 years later I finally took my climate control apart and fixed the fading digits problem. In fact, whoever had said there was a connector you could clean was correct. The LCD display has a row of pins on it that fit into a "socket header". Getting the climate control out and apart is another matter, but once you do and you pull the LCD display out of the socket, you will be able to see little dark spots of corrosion on the pins (with magnification). I carefully scraped the corrosion off, maybe it is more like oxide than corrosion. Anyway, then I put a little silicone grease (same as dielectric grease) on the pins to hopefully ward off whatever was making them oxidize in the first place.

Put it all back together, put back in the car and works perfect now!

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1998 C230 330,000 miles (currently dead of second failed EIS, yours will fail too, turning you into the dealer's personal human cash machine)
1988 F150 144,000 miles (leaks all the colors of the rainbow)
Previous stars: 1981 Brava 210,000 miles, 1978 128 150,000 miles, 1977 B200 Van 175,000 miles, 1972 Vega (great, if rusty, car), 1972 Celica, 1986.5 Supra