Hi Benjamin,
Take a look through this recent thread: XK120 Dynamo / Generator, Voltage Regulator problem - #9 by Nickolas.
There is a link to a Lucas document explaining in detail how the regulator works and another one in the thread that goes into detail about testing the generator/regulator set-up.
The first place to check is the regulator relay contacts. The cut-out coil should only close when the generator is producing enough voltage to charge the battery - so it may be this relay’s contacts that are not functioning. The other relay is to regulate the field coils of the generator - these are normally closed, opening when the generator needs to be prevented from producing too great a voltage/current.
Check all connections, particulalry the ground/earth connections. Also use an analog meter to measure voltages - digital ones will jump around.
Regards,
Clive.