' The alternator output wire joins the harness
and travels back to the cockpit engine panel."
That might NOT be the output wire, the output shouldn't be going back to the panel at all, as far as I know. There SHOULD be one or two wires from the alternator going back to the panel, but they would be the excite voltage and key switch that tell the alternator "OK, turn on now".
On many alternators
, the output wire is a single heavier wire connected to a stud all by itself, and the other 2-3 wires will all be connected to one wire connector/plug.
Something to doublecheck.