The tach gets its signal from the lighting coil.
One part of the sleds wiring harness should be constantly "hot" whenever the engine is running....that is the circuit to the brake light and the tach.
Obviously, the brake light has to work with the key switch in the "on" position, or the "on/lights" position.
Is your brake light working properly with the key in either position?...if not, you may have to check the wiring underneath the seat....it may be worn through and shorting everything.
Or, you are really unlucky and you have 3 bad tachs.
An electrical multimeter should show some AC Voltage at the plug for the tach with the engine running.
If the brake light works, it has to be "dead" tachs, or a problem with the wires (or connections) to the tach.