Aha, now we are getting somewhere, perhaps.
It has nothing to do with a lack of conventional fuses, the smart charger or much else of a 'modern' origin.
More than likely you have a simple short in the left hand indicator switchgear, maybe broken or simply dirty. Failing that, in its leads.
From memory, the park light sequence is initiated by the left hand indicator and the ignition switch. If the switch is shorted to on, when you turn the ignition off, the bike will light its park lights.
The chances are that the BuMW charger is not sufficient to charge the battery and run the park lights, so the battery flattens itself.
Start by simply checking / cleaning the switch connections and / or do a search on UKGSer. There are several threads.
If the bike is still under warranty BuMW may well do the job for you and / or replace the switches for free. If it's out, get busy or pay or ask for a goodwill payment.
PS It might be interesting to know how many people who have flat battery problems on the 1200 GS have exactly the same problem. Ie. They have initiated the park lights and wandered off for a couple of weeks. Then come back to a dead bike.