Oh, duh. That is the exact same diagram picture as mine (or as it was originally, I updated it), such that I didn't even notice the difference. But the funny(?) thing about it is that the R/R they say to use won't work with it. It's only a half wave rectifier. I tried a couple of different rectifiers, and only ever got 6 volts out of them, before I figured out what the problem was.
On an earlier incarnation of that project, I was using a 50cc 2 stroke Shindiwa clone, that I upgraded with an electric starter made for it. Interesting starter, it used the crank of the engine directly, as the crank for the starter "motor", which was really then just a stator around a wheel on the end of the crankshaft of the engine, so it was direct. I found that when the engine was running, it made a decent 12v charge, DC. So I connected it to my battery through a diode so it wouldn't crank the engine, and wired the start button to simply bypass the diode. That actually worked, and charged the battery. I was pretty impressed with myself on with that one.