From what I've experienced here (same with the other Disney site), if you actually go to your user name up top and purposely log out, your light goes off at that time, and will show as such as soon as you switch/refresh pages. If you don't purposely click "log out", even if you shut your computer down, it will still show you are logged in 'til it times you out in about 20 min. or so from your last activity.
Funny thing is, one day last week when I pulled up this site at the office, it still showed me as logged in, which isn't unusual if that's where I left it the day before and didn't click "log out". I figured it would do what it usually does and show me as logged out as soon as I clicked on "recent posts". Nope, I was still logged in. Never had to log back in. Never had that happen before.
And, again, you can disable the light, altogether, in your settings.