First off, I have a 2002 Malaguti F12, (not stock of course). I am an auto mechanic but I am finding moped to differ a bit from cars. ;)
My electrical starter stopped working; I thought the battery died being over a year old. So I bought a new battery, and still the electrical starter didn't work. I also noticed that all my lights, horn, ...well everything that runs off the battery only worked when the moped was running. The faster the engine speed the brighter the light or the louder the horn. Just as if the battery was dead, but it's new and I had the new battery tested and the new battery is fine. I bypassed the starter to see if it would crank and it did. I checked the main fuse and that was ok too. I think this might be the voltage regulator but I’m not sure, and I don’t want to just start changing parts that I don’t need to.