If I just close my browser or Cadillacforums tab, how long does the site continue to show me as 'online' with a green dot next to my name on my posts?

I presume if I actually logoout of the site, it changes to offline right away.

No rhyme nor reason - sometimes you'll stay logged in for hours, sometimes just closing the browser logs you out. I would always log out as a courtesy to other members: the more in the site, the slower it gets. Nature of the beast.

The online indicator doesn't shut off right away. It has something to do with the new post indicators as well. I forget the specifics, honestly...