New rider

[bwinge250]

Hello! I'm a beginner rider and recently purchased my first bike, a 2007 gz250 (I rode a 150cc scooter for a couple years but finally upgraded to the clutch). I've had my bike for about two months and am an almost-daily city rider, and it's absolutely perfect for me. Just one problem though...when I bought the bike it ran great the first ride but wouldn't start after that. The seller said it had been sitting for awhile in the winter months, so I figured he just hadn't kept the battery maintained and sure enough with a brand new battery the bike has been great ever since. However, about two weeks ago I noticed that the dash light for my blinkers wasn't working. My blinker was on but the little green indicator light wasn't. The next time I rode, though, the light worked fine. I've also noticed that on occasion, the green indicator lights for neutral and the blinkers will fluctuate between being really bright or really dim, with no apparent reason. Then one night I shut the bike off but my brakelight was still on. I turned the ignition switch to on and then back off and the light went out and everything else was normal. The only other thing I've noticed is that every now and then when I'm sitting at a red light the bike will rev up in RPMs just a bit. Not much, but enough that I notice. We've had a lot of rain so I haven't ridden for about a week, then went to start the bike yesterday and it's dead again. All the lights are on and bright, but there's just not enough to turn the engine over. It whines for a couple seconds but then quits. I put it on the charger overnight, but still won't start today. This is exactly what it did when I bought it two months ago. Something has to be killing my battery since this one was brand new. I'm planning to take it to the local Suzuki dealership because I don't know anything about the mechanics, but thought I'd check to see what you guys think. Does this sound like a wiring issue or an "alternator" issue, maybe something with my charging system? I'm hoping it will be an easy fix....

Thanks!