A great way to restore a dirty guitar fingerboard is to give it a good scrubbing with some 0000 steel wool. (This is not recommended for finished fingerboards like those found on some Fenders and Rickenbackers, unless you want to remove the finish….)
The problem is that steel wool leaves all those little steel fibers that seem to immediately fly straight into the guitar’s magnetic pickups, where they’re impossible to get out!
The solution: Use gaffers tape or masking tape to cover the pickups before you steel wool the fingerboard. When you’re done scrubbing, it’s much easier to get the steel fibers off, either with a vacuum cleaner or just use another piece of masking tape to cover over the first layer, peel all the tape off the pickups, and throw away!