Congrats on the new bike, and congrats on taking the effort to give it some TLC!
I was under the impression that if you're only using your kick start, that has nothing to do with your sprag at all. Someone will correct me if I'm wrong, but I thought that a busted sprag, although potentially jamming up the system with broken teeth, etc, wouldn't be in use while kickstarting, and that it couldn't be the reason for the intermittent kickstart lever.
I also wouldn't pay any attention to a neutral light (or lack thereof). Mine works about 5% of the time, and it's just coincidence if the finicky light decides to turn on or not.
That being said, I may have a lot of posts on here on the forums, but I'm still a beginner in a lot of things motorcycle. For instance, it seems strange that this problem you're having is intermittent. If it is a clutch tightness issue (clutch cable connected to the hand lever is too tight), could this maybe be aggravated by the handlebars being turned to the far right? Not sure if the clutch lever is the same, but I know this can be a concern when setting the tightness of the throttle cable. (turning the handlebars to its extents can put additional tightness on the throttle cable, which would be noticeable by the engine revving when you're not twisting the grip) just wondering if that same thing could be at play with your clutch cable.
Either way, checking your cable tightness and maybe 'clutch throwout adjustment' could be simple things to check, even if to just eliminate them as problems.
Also, how is your electric starting? You mentioned that the battery is low... if you don't have a battery tender, just try hooking it up to a car's battery with jumper cables to charge it a bit. Make sure the car is turned OFF cause i've heard bad things can happens if it's on (overpowers your old fashioned bike electrics). You could leave it hooked to the car's battery for a bit and see if that helps charge it, or you could just try electric-starting your bike while jumper-cabled to the car. If it starts fine every time, then you know your sprag is OK.
Lastly, one thing that happened to me (embarassingly) is that the little bolt and nut on the bottom of your kickstart lever got loosened on mine and I didn't notice it. Then when I'd kick it, it would sometimes work fine, then other times it would slip right down... this was the metal kickstart arm slipping on where it connects to that round nub that protrudes out of your gearbox. I'd have to pull it up again to try kicking again. This only lasted a handful of kicks though til it was totally shot... The little teeth on my kick-lever got sheared off and I had to replace it. Luckily a generous forum member sent me his old one for simply the cost of shipping. I'm guessing that's not your problem but it's at least something to check.
Lastly, I'd listen to Ice... he's got it narrowed down a bit and i'd guess that one of his suggestions are correct. I type a lot but my actual know-how is fairly limited. This AVL is my first bike, and I've never done anything mechanical or automotive before getting it three years ago.
Cheers,
chuck