A simple question first.....How's the battery?
So many times guys over look this simple element!
Is this a Ducati?
I would get hold of a service manual so you can go through all the
electrical trouble shooting steps.
There are always several resistance tests you can do to find the fault,
sometimes they show where it lies and sometimes not.....I've seen
bad stators that show resistance within spec....so who knows.
The batt may test at 12.5 volts but could have a bad cell and causing
problems.
But your system should be putting out about 14 volts as you've pointed out.
So who knows. But a good battery is very important so that the other
components can operate at spec.
Also look for any corrosion, clean all connections, tighten all connections,
look for frayed or abraided wiring looms, split sections, bad kinks, missing
or unplugged or bodged plugs or wires.
Good luck!
Patrick