I post on this forum for my 750K but for whatever reason can't get this post approved on the Hondatwins forum so I'm going to try here...
Starting to pull my hair out with this one... Google/forum searches get me info on testing batteries and charging systems, but I don't think that's the right direction to go.
1972 CL350. Mechanically the bike is stock (engine, carbs, air filters, exhaust). Electrically, almost everything is new (wiring harness, solid state reg/rec, PAMCO ignition, LED headlight and tail light, new turn signals, handlebar switches, coils/wires/caps/plugs, brake switches, LED idiot lights, Motoscope Mini gauge). The only original parts would be the stator, rotor, neutral switch, and starter and solenoid. I bought it in October of 2018 and the seller said the battery was new (of course!), but I believed him and it looked it. It would start just fine, but I noticed the headlights would be pretty dim at idle and it did stumble off and die in neutral. I had a similar issue with my 750K that a new AGM battery solved, I know the battery needs to basically be perfect for these to run right.
I bought a new lead acid battery and it seemed like it ran better (at this point I now rebuilt the carbs, replaced both slide diaphragms, and replaced the carb insulators/manifold), but it seemed like every week when I'd go to mess with it, the battery was dead, so I started leaving it on a tender. Even then, I'd get maybe 2-3 seconds using the starter, then it would start to slow and the lights would flicker, like a dead battery. I'd constantly be recharging it, and if I just kickstarted it it would run decent enough around the neighborhood (still haven't gone on a long ride yet because I don't want to get stranded). Even though the battery was new, I was convinced that maybe it was defective, so I bought a new AGM battery from Motobatt and installed it Thursday, and the symptoms haven't changed.
The only other thing I thought to check was the cable from the solenoid to the starter. I broke one of the terminals of the original last year, so I bought a 6AWG ground cable at Walmart and appropriate sized terminals and made a new cable. I checked voltage at the starter when turning it over and saw about 9.6 volts max hitting it, and the loss was between the solenoid and starter. I cleaned all the connections and saw the voltage go back up to 12.6ish, but still the same problem. You'll get 2-3 seconds of solid engine turning over with the starter, then it slows and the lights flicker. If you kick start it it will run just fine, but if you shut it off and try to restart it with the starter it barely turns over if at all, and the lights dim.
Not sure if this matters, but I did do the yellow/white wire mod so the stator halves are always connected, and I don't have a kill switch, I just jumped the wires. Also, I had a spare 'generic' solenoid that I bought for my 750K and put that on, and all it did was click once, but no power went to the starter. I put the original back on instead. Not sure if any of those have anything to do with anything or not. I really want to love this bike, I've wanted a scrambler for so long, it's just getting really frustrating. I went through the same thing with my 750K which is now my daily rider, so I know there's light at the end of the tunnel, I just wanna get there!