This isn't directed at you especially, in that lots of people do it - just a broadcast message:
This is not a fluxbox problem!
People would probably get better and faster help if they'd correctly identify the issue. Flux may be what prompts awareness of the problem, but you need 'gdm help'.
Now, I don't know anything about gdm or redhat - I clicked on your thread because it said 'fluxbox'. If you can execute from runlevel 3 like that, though, you should be able to create or modify an ~/.xinitrc whose *last* line is 'exec fluxbox' and then do 'startx'. That way flux will be controlling the session rather than the terminal emulator. Then you can close the term without closing the session.
See if you have an xinitrc anywhere on the system you can copy and modify if you don't already have the dotfile in your home directory. And I hear there's a thing called 'switchdesk' on RH - some people seem to have trouble - for some people it works. I don't know. As far as adding to a graphical login prompt, though, I really don't know - completely forgotten those, though I did use one on my first install and had to disable one on Debian not long ago.