Be careful if removing the tach. The current cluster in my car is made from 3 different clusters. The seal at the top of the housing eventually becomes brittle and crumbles apart; moisture gets in and starts corroding things. The screws on the back can sometimes get rusted into the terminals on the tach unit itself, and they'll break when you try to get it off. Some good penetrating fluid with one of those straws works wonders there.

Check your connections to the ignition coil. I've heard that a corroded connector somewhere in that system can cause tach issues as well.