Severe voltmeter needle oscillations

Francois, I am thinking that you have a problem with your ignition switch and/or associated wiring. There is a welded splice under the dash that contains the battery, alt, amp gauge, headlight wires AND ignition switch feed. Once in the steering column, there is an accessory feed in the harness that that sends power out to a smaller splice. This smaller splice feeds the wipers, accessory terminal (where your gauge is plugged in)on the fuse block and the 12v dash supply (I suspect that your gauges don't work with the rest of the aforementioned deficiencies). If it were me, I'd wedge a test light into the back side of the 12 gauge black wire coming from the ignition switch (on the vehicle side of the plug) and go for a ride. When the voltmeter is reading voltage, the light should be on. When the voltmeter goes to 0, the light would be off. To me, this would indicate the problem with the feed coming from the ignition switch.

Take my suggestions at your own risk :)

Good luck