I just got a z31 1988 Turbo decently worn by the previous owner. Was driving it and a bunch of the dash lights came on at once. Battery, brake, radiator, and lights. They stayed on but would dim out and go away once I came down to a stop. Then would glow back to brightness as rpm increased. Another time when I started the car it was the opposite. All lights on and they dim out as rpm goes up. I believes its electrical issues but I don't fully know where to start apart from checking fuses.

Get your alternator checked I have replaced mine 2x's since buying car new in 84' and I remember that being the issue. You can get it checked quickly at any place that installs batteries.