You may have noticed that I am a little suspicious of the ST2 electrical system. I have been used to riding BMWs all my life and those bikes have high capacity electrical systems when compared with the Ducati. I believe that this can be made more reliable by reducing the loads on the system while bringing the bike up to date with things like low power LEDs. The other thing that would be useful is to be able to monitor the system, the best way being the use of a voltmeter. The battery is only on the bike to start it and has no function when the engine is running, the power should be supplied by the generator when running, and as long as that generator is putting out a higher voltage than the battery is, it will be charging that battery and powering everything else.
This is the voltmeter that I bought from ebay for less than £4 (€5). Link
It fits very neatly into the panel just above the fuse box and is tapped into a wire that is only live when the ignition is on. Before fitting I checked the accuracy against my garage voltmeter and found it to be good.
Here the engine is running, with the cold start lever on, at 2000rpm. noting is switched on apart from the Front LED marker light and the voltage is reading 14.1 volts. That will be chucking power into the battery that will be a little depleted due to having just started the engine.
This was taken a few seconds later with the HID xenon headlight switched on, showing 13.7 volts. The additional load is: 35 watts headlight, 2 watts tail light (LED), and about 3 watts for all the instrument lights (LEDs). As the battery will have a little more charge than in the last picture the regulator rectifier will also be lowering the voltage automatically.