The faulty wire is the contact mechanical part between the alternator and battery.This may cause a short in the electrical wiring which may cause the alternator to show low output.
The wiring could be malfunctioning causing it loose power between the two. Another thing to think about is a problem with the sensor. It can be tricky to determine this with out testing everything separately witch you have already done.
You probably have a wire that is grounding out due to an exposed wire to a metal part of the car. Tracing and replacing wires that should do the trick.
There should be nothing between the battery and the main charge wire of the alternator. If no one has added accessories and cut into the wire and both components test fine I would suspect either the battery connect or the gauge in the dash itself.
