Interesting depictions of what is and what is not a one-wire alternator.
For about 20 years, I have been using a JC Whitney 1-wire alternator on a 1954 truck that I converted to 12v. Yes, it is "self-exciting" - at around 400-600 RPM. Thereby, it starts charging every time we start that truck - the fast-idle/throttle and choke at start-up allows the engine to briefly reach 800+ RPM.
Here is the wiring diagram I found/use - found in the early years of the public-Internet.
