I had the problem you describe when I bought my bike, a 350f. Probably basically the same thing. It'd drain flat with the headlight on, but run forever with it off.
It ended up being the connections to the rectifier. There are 3 yellow wires and 2 others, maybe a red and black (diagram on this thread shows it as red and green, that may be the case). Anyway, assuming your bike is the same as mine, the shop manual gives instructions on how to test that your rectifier works using an ohmeter. I took mine apart, noted that the connections weren't the stock connections and weren't great. I did the ohmeter tests and found that my rectifier works fine. When I reattached it, I got new connections and used dielectric grease, and it's worked great ever since.
What voltage do you get at your battery terminals when you are at about 3k rpm? I would think at that level you should be almost up to 13.8.