Maybe this will help. I have a Yamaha DT250, and it's headlight and gauge lights are powered by the alternator, and the tail/signals/horn are powered by the battery. This leads to some some circuits only working with the engine running vs. some not. Also, some reacting to revving vs some not. You have a different machine, so those details may not match-up, but you might have similar circuit separation going on.
Here's a (unfortunately black and white) wiring diagram:
https://www.classiccycles.org/media//DIR_1653304/DIR_1792956/7b4ebf4db60cffe5ffff81d6ffffe417.pdf