Hi Nate,
Sorry to here you are having electrical gremlins. I saw in a previous post that you were having the lights go bright and dim at random. What you are describing sounds like it may be related. There is nothing under the seat that is mechanical in nature to cause a noise like you mention, the radiator overflow is mounted in near the horn on your bike. I suspect that the same problem that is causing your lights to go up and down is overcharging the battery. The battery will boil if overcharged and emit a lot of hydrogen gas (be careful not to create sparks, hydrogen is very explosive) that may be causing the whistle noise while escaping the battery. I think you should just go ahead and pony up for a new voltage regulator (lots of threads on this board for that subject).
Good luck,
Russ