Engine not running:
Personally I would hook up the Voltmeter to the battery and watch the meter as I pull one fuse at a time. I you pull a fuse and the voltage rises you have identified a possible circuit that there could be trouble in.

Do the same but disconnect the wires from the Alternator or if it has a remote regulator from the regulator.

Get in close the door buckle up and stick the key in the ignition. Don't attempt to start or actually turn the key but stick the key in the Ignition and slowly giggle it around while watching the voltmeter for changes in voltage.

This is an odd one. On my Mothers Car the top of the Battery got so dirty and scummy that the scum was conducting some electricity between terminals. It was magnificent because she often walked to work and when she did drive the car it was usually for less then 5 miles round trip.
I was probing with the voltmeter and stuck one probe into the scum and I got some small number of voltage (this was back in the 1970's so I don't remember the reading).
I cleaned the top of the Battery and She stopped having it cause issues. Note Batteries back then were not as well sealed as they are not.

Charge the Battery and take it to be load tested just to be sure it is not the Battery itself.

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84 300D, 82 Volvo 244Gl Diesel