If the alternator quits or looses ANY connection the tach will be the first to jump, flick, or quit. This includes the large charge wire being loose on the back of the alternator. IMO alternator isn't the issue.
Voltmeter dropping into the red:
Lets be clear that it is hard to drop two 850 CCA batteries and a 100+ amp alternator into the red on the voltmeter. It takes a 60+ amp load like glow plugs to do so.
Bad ground or power to voltmeter including the gauge cluster. This means pull and clean fuse contacts.
Bad, cracked connection, bad gauge, or other issue in the gauge cluster.
Bad ignition switch causing a "brownout".
Glow plugs, starter kicking on, or big short dropping voltage.
Let me expand glow plugs - yours should be ECM controlled, but, older ones and weird stuff can kick them on with loss of connection(s) to the controller. Likely at this stage you have a big short vs a bad starter or glow plugs coming on, but, fiction has to be plausible - the truth does not.
Bad battery or two.
Be aware the fusible links get old and can fail.
Wires can corrode internally.
Other things can drop voltage like rolling down a window or short elsewhere unrelated to the gauge, but, getting power off the ignition switch or same power feed.
Wiggle test with someone watching the gauge. Wiggle every harness - be careful as a bad (high resistance) spot can be hot enough (or suddenly get hot enough with hitting a short) to burn you. (Wear gloves and/or use a IR temp gun on the harness to look for hot spots.) Check the battery tray where the positive cable passes it for a intermittent short. Model year dependent the main power wire goes by the starter and is subject to insulation falling off causing a short.
Shorts as I refer to above are the hard to find arching shorts at less current than will burn the fusible links, burn the wire up, or burn the vehicle to the ground. These would be the easy to see and find failures.
Sometimes the price is worth admission at a good auto electrical shop to have them track down electrical issues.