I think that disconnecting the terminals or removing the belt causes the same effect : preventing the ALT to send current into the circuit. Am I wrong? I don't know
Removing the belt stops the alt from spinning BUT the field wires are still hooked up and the field is drawing current.
By disconnecting a field wire the field is no longer drawing current.
From the looks of those wires I would not trust any of them.
Still your symptoms do not point to the charging system they point to bad wiring somewhere in the system.
The VR and the alternator match so that is good BUT you should check that the alternator is really an isolated field alternator.
Easy check... Disconnect both field wires from the alternator.
With a multi meter check to see if there is resistance or open or short to ground from each terminal and ground.
In an isolated field alternator both field wires should have no connection to ground ( many meters display this a OL, basically what the ohm meter reads when the leads are not touching each other.)