I know this is an old thread but my 84 had the same issue. It was an issue with the dash itself and the only solution was to remove the dash out completely and I replaced it with one that was reworked by a local shop. That was about 5 years ago and the new one (knocking on wood) works great.
This ins't a trival replacement, I have a local shop in LA that knew how to do this, you'd need to find a local guy that knows these or buy a new one that you know is going to be solid. there is a site where you can buy a used one that will match. This site will help
http://www.300zxpartsforyou.com/
then you just have to find someone that can do the swap out.