Hello.

The switch doesn't need to be grounded. The problem that you describe is almost always one of two things. Either a factory tach that has died or an issue with the resistor wire. There should be a red wire with a green stripe coming out of the connector on the back of the ignition switch that is only a few inches long and plugs into a fat pink wire with some black insulation on it. The fat pink wire goes to the firewall connector and, on the other side of the firewall, turns back into a red wire with a green stripe that is attached to the positive post on the coil. That's how the coil gets power when the key is in the 'on' position. It could be that the pink wire got unplugged somehow, or has burned out or something, but, that's probably where the problem is.
