Sam, regareding the generator, warning light, and tach.
At slow idle, usually the warning light will NOT go off. At slow idle it does not usually put out enough voltage to charge the battery - so the light stays lit. That's one of the reasons for the switch to Alternators- they put out more volts at idle.
Both sides of the warning lamp should be "hot" relative to ground when the ignition is ON. One side is connected to essentially the Battery voltage. It should have the same voltage as the car's ignition, lights, etc. The other side of the warning lamp is connected to the generator output. At slow idle (or not running) this generator output voltage is less than the battery voltage, so the control box disconnects the generator from the battery. Since one end of the lamp is at about 12 V, and the other end is at some less voltage (or 0 if the gen is not turning at all) there is voltage across the lamp, so it lights. Once the generator is going fast enough to put out more voltage than the battery, then the control box connects the generator to the battery, and the battery, lights, ignition, AND generator output are all at the same voltage. Now both sides of the warning lamp are at full operating / charging voltage (about 14.5 V). with both sides of the lamp at the same 14.5 V, there is no voltage across the lamp, so it does not light up.
I am 99% sure there is no correlation between your tach misreading and the warning lamp being ON.
Tom