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Hint Numba 1 - vent it. It isn't necessary to go the gore-tex route (although this would be nice). A single hole drilled in the back cover of the instrument cluster between the rows of pins will work fine, and be in a spot that doesn't get wet. Disassembly of the instrument is recommended so you don't drill into the guts.
Hint Numba 2 - seal it. This hint came to me from England - and if they don't have moisture I dunno who does. After you add the vent above, and reassemble the cluster - carefully replace the useless "O" ring in the groove between the halves (it isn't REALLY an "O" ring - it's a foam ring..). Then using HIGH QUALITY (3M can't be beat!) electrical tape - run a single layer of tape over the joint between the 2 halves. This will provide a very effective seal, and when mounted on the bike (especially on an RS or RT) is virtually impossible to find (and if you do it neatly - it looks like it belongs there).
Having done the above - my K has survived downpours, cold weather, hot weather, rides in the rain - and has never fogged up again.
Not a bit - really!
Cost - about $0.10 worth of electrical tape.
The instruments plug into each other and the main circuit board mostly using square pin connectors into square sockets.. your job it to make these connections good electrically, and prevent future corrosion.
Remove each component of the cluster with care - they unscrew and unplug. Haynes manual shows the process of disassembly.
Clean the connections as other people have described. On badly corroded connections - a bit of scraping with the edge of a tiny screwdriver until some bright metal is seen will help.
Then - the trick stuff:
Trick numba 1 - VERY carefully - take a good quality small pair of pliers (I would use ones with a tip about 1/4" wide, and narrow ends), twist each square pin about 5 degrees (direction isn't important). Be very careful not to damage the plastic they are mounted in (using two pairs of pliers is even better, hold the bottom of the pin near it's mount and carefully twist the top just a tiny bit.
What you're doing here is adding pressure to the connection, and exposing 4 sharp edges of the pin to the inside wall of the sockets, improving the electrical conductivity of the connections.
Trick numba 2 - (and thanks to Brian Curry for this one!) find your metallic based antiseeze and a toothpick. Goosh (tech term again) some antiseeze out on a clean surface (not much - you're only gonna use a tiny amount, and it is messy stuff). Take the toothpick and pick up a tiny amount of the antiseeze. Push it into one of the square sockets. Do each one, with only a tiny bit of antiseeze.
What you're doing here is two things:
1. Filling the voids so oxygen can't get at the nice new connections you've made by doing hint numba 1. Some people have advocated using greases such as silicone - these are non-conductive, which isn't good...
2. You're increasing the conductivity - yep! The metallic based antiseeze is conductive. It's the metal in it. (Usually either copper or aluminum).
Reassemble as per Haynes, reinstall and enjoy working instruments... unless you have a '85 - in which case I'd suggest removing the fuel warning lamps (they don't work worth a damn when they are working) and installing a FuelPlus+ - which is when I did all of the above!
The bending of the pins may have been an official BMW repair technique.. my pod had been repaired when the bike was about a year old.. and it continued working even with the severe fogging I experienced with it. The antiseeze is the icing on the cake.. too bad motometer didn't do it at the factory and use something besides a swiss-cheese rubber ring to seal the things with!