Hello, my name is Mark and I will try help you with this.
I suspect the fault is due to either a corroded or partially broken exciter wire connection.
Corroded wire connection will pass voltage but not current which is probably why you are getting a low voltage reading but there is not enough current passing through the alternator to allow it to start charging.
When you give it an independent 12v feed it works so this suggests a fault with the exciter wire.
Check the wire at both ends if possible for signs of internal breakage or copper corrosion, (turning green)
Do you know where the other end of the exciter wire goes too. I've checked the alternator end and all seems ok but when I try and trace it back it goes into part of the loom and i'm having trouble tracing it?