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The earth wire that connects to the alternator is not there to earth the alternator as such. The alternator's main earth is via the engine and then via the main negative battery cable.
The other end of the black wire connects to a couple of body earth locations. So I don't think this is your problem.
If you disconnect the two pin plug from the alternator does this turn off the battery gauge and red lights?
Is the original plug at the alternator still used or has this been replaced with single connectors?