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Others know much more, but I would expect that your tach would operate off the primary circuit to the coil, not from the Hall Sensor signal directly. Therefore, no tach movement really only tells you that there is no primary signal to the coil. There has to be an amplifier somewhere between the hall sensor and the primary signal.
I think that your other question relates to wire from the ignition computer to the fuel pump relay. I have forgotten the exact logic, but I think that the idea is that it will cut the power to the electric fuel pump after a few seconds if it expects to see an ignition signal but doesn't (i.e. key in Run position) so that you don't pump fuel out on the ground after an accident. When our Hall sensor failed, we had to short-circuit the fuel pump relay to start the car and get that system to reset itself after the repair.
If you have been fighting it for a while and the electric fuel pump is still working, then the problem must be somewhere downstream of the computer, but before the point where the tach ties in. Perhaps the tach or it's wire has failed and is shorting the primary coil signal to ground?
I just wrote a lot of words and didn't tell you anything useful, huh?
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