On Fedora 8 and later or Centos 5 and later
In a X11 session, run gdmsetup. Go to page 2 (remote) and tick "Same as Local". Close gdmsetup. Open it again to make sure it saved, Sometimes it needs to be done twice.
To set up Clients
On Thin clients, you connect this using a X11 or xdmcp configuration.
On Backup computers that are rsync'd from the main computer, Go to gdmsetup, page 3 (Security). Click on Configure X server. Modify VT0. Change type to "Terminal". In the Options, add "-query <IP.Address.of.Server>". Restart the whole computer for it to take effect.
To undo this, and make it a normal server: edit /etc/gdm/custom.conf . Delete the whole line with your -query option above. This has to be done when converting backup computer to main.