Hello, all!
I put distilled water in the battery.
I tried to start her up, and she started! Yay, a little progress.
I started her 6 times:
1) Backfired a lot! But started up. No trouble turning over, rough idle, she idled for about 5 minutes.
2) Started up again, idled, then died.
3) I got the idea to play with idle mix because she was running so jaggedy and rough--stopped idling. *newbie error*
4) Wouldn't start--nothing, not even a click or sign of life at all.
5) My neutral light flickered on and off several times, then she started up rough, idled for about thirty seconds, and died.
6) Rough start and died, short run.
Yes, I realize I probably shouldn't have played with the idle mix while trying to diagnose issues--newbie mistake. (!)
There are other observations: my negative terminal battery bolt doesn't cinch, it just spins around. Which likely accounts for the neutral light on/off situation? It seems to missing this square nut piece:
https://www.amazon.com/BikeMaster-Battery-Bolt-6x10mm-Rectangle/dp/B004C1ZRMO...So, some progress, but there are still some combination issues here.
I'm going to get that part for the battery and see how much better it gets. And likely charge the battery.
Any other thoughts or things I should be checking on are warmly welcome and genuinely appreciated.
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Image of terminal here:
http://imgur.com/a/ihV2v