hjo wrote:
It's got a Piaggio Badge, then a hex one with BB?

That's an older Bajaj logo. I'll wager the ignition can be switched over to a ducati unit. That said, if the current CDI is working there's no cause to switch it out. There's nothing fundamentally wrong with this setup.

If it fails to spark I would expect a problem on the stator plate or simply faulty wiring ahead of the CDI.