ITs more then likely the SI board or the SI board rechargable batteries. The is this thing inside teh gauge cluster called the Service Indicator board. It turns the little red, yellow, and green LED lights on in the guage cluster, there right below the check engine light. The SI board has rechargeable batteries in it that go out. Or the SI board could be fried. You can still get replacement SI boards from bmw or parts houses. This little board is suppose to tell you when to change the oil, green lights for good and red for bad obviously. All it does is watch how many miles you put on the car and what rpms the engine mainly runs and calculates when to change the oil.
The Tach and the Temp guages do not work in my car, and I am going to tare apart the cluster and try replacing the batteries... I hope the batteries are to blame, otherwise its the SI baord.
I highly doubt it is any fuses or connections, this is just what happens to our E30's. I have owned 3 E30's now and all have had guage problems because of the damn SI baord. Glad bmw dumped the idea after the E30.
The si board and the timing belt are the only stupid things bmw did on the E30, IN MY OPINION. Our engines are the ONLY bmw engine(to my knowledge) that has a timing belt. I would rather have chains.
Later guys and gals.