The answer to most electrical problems is to start by checking the earths in the car. The battery is usually connected to the engine by an earthing strap and the engine is separately connected to the car chassis by a further strap. All connections should be made to clean bare metal and a light coating of grease on the connectors can assist in keeping contacts clean. The connections should all be tight. The instruments tend to have a separate ground located somewhere under the dash and it can be a tricky exercise to locate it.