My 2005 (20k miles) does this loud enough I came here looking to see if it's normal. Mine is annoying and (to me anyway) conspicuous while sitting on the bike. I think the whine pulses with the turn signal on mine too at least sometimes.
Got my FZ6 yesterday and found/went to register for this site today.
The register links on the main page of the forum point to what I guess is an old domain for the forum.
Anyway, they point to:
http://www.fz6-forums.com/forum/register.php
I changed it manually in my browser to...