Even though the tach seems to be wired correctly to offer any reading, I too suggest you REALLY check the voltage and ground wires going to the tach, AND the signal wire from the engine itself. So many times a corroded connection offers proper voltage readings until vibration gets going. So first thing to do is trace the tach wires to their source(s) and remove, clean to shiny metal and reattach those wires. Then see how that works. You maybe surprised...
If then you still have an issue, come back and tell us. There could be other issues inside that tach itself or even with the signal source. JMHO