[Oldsguy]

Welcome to our site. I would venture a guess that you may have a bad turn signal switch or headlight switch or wiring since you said it stays on all the time when the headlights are on. Either one of those could be causing a "soft short" to ground which would drain your battery and work against the charging system. This could also explain the "gen" light being on all the time. Remove the fuse that protects the headlight circuit and see if your gen light stops illuminating. And the same with the turn signal fuse (if it isn't the same, not sure). This will at least narrow down the problem some. There could be other troubles as well, bad grounds, worn wiring someplace, the list goes on and on.