Craig - you've done a good job in trying to understand Huib's post for which thanks.
Like you, I have no knowledge of this model.
Huib's question about the purpose of the red wire on terminal 2 is difficult to answer because I can't read the ignition switch/kill switch details on the wiring diagram.
I did think it might just be a mechanism to kill the engine and stop it from being started without an ignition key. In other words, the alternator provides a magneto type AC output to the electronico box which directly fires the coil and plug. So no battery / 12v supply needed. But I'm not sure that is the case - it may be that the box does need a 12v supply.
1. From my reading of the wiring diagram, you don't need to have the battery connected.
What I think happens is that power for the ignition system is provided by a feed coil on the alternator. This is a very common system used on lots of small capacity engines.
Here is a typical example which seems to match yours*. Note that in this drawing, the feed coil is called a "stator coil". Also, the wiring colours seem to be different from yours; so you'll have to allow for this.
Obviously if this "stator coil" isn't working, it will produce no power and the ignition won't work.
Start by trying the test suggested above -" 50V AC between the 'green' and 'white' wired when cranking". "Cranking" means kicking the engine over.
You will need to work out which wire is which since, as I said, it seems the wire colours don't match the Laverda installation. And note that it's AC volts NOT DC, so set your meter appropriately.
If you find the coil IS producing electricity, check the pick-up is working by measuring its resistance using an Ohmmeter as suggested above.
2. As to the red wire, that would seem to be the green wire in the diagram above. It's a control wire connected to the ignition ("key") switch. How this works on Ducatis is this wire is used to turn the ignition OFF by grounding the ignition feed from the "stator coil".
* Except there's no "modello elettronico". I still don't know what that does ...
No worries. Since the post you picked up on, I've added another which may be a bit of help to Huib. I strongly suspect Laverda would have used something similar to the "Piaggio" system shown in the illustration and which was very common at the time.
But what the "modello elettronico" does, escapes me