"Remote X session" option?
 

I seem to recall that when logging in, using GDM I think, I would see an option to log in to a remote X session but I no longer see it.
Is there somewhere I can configure GDM or LDM so that I have an option to start and X session on another machine?

this link is a bit old, but I think you can start with it: http://www.yolinux.com/TUTORIALS/GDM_XDMCP.html.
Otherwise google is your friend, try: "gdm remote login"

Thanks, I've tried googling but most results either seem out of date or use an additional program like xnest which isn't what I'm looking for. The link you provided is a typical example -- useful but only half the story.
As far as I can tell I know how to set up the gdm3 to allow remote displays but I can't find the settings to give the remote login option on the greeter.

can you specify the version of your os, window manager and related softwares

Sorry, should have said, both machines are running Sid with XFCE4. Both are running gdm3 3.4.1-1.