How to run a daemon process only when xfce4 session is running?

[Chris Green]

I have a background process that I want to run only when an xfce4 GUI
session is running but I can't see a way to do this.

Putting the process in the 'Session & Startup' list in Settings starts
it OK but the background process never stops.  Thus if I log out and
then log back in I get multiple copies of my background process
running and that causes all sorts of issues.

There doesn't even seem to be a logout equivalent of .xprofile where I
could run something that kills my daemon.

This background process is just a shell script.

-- 
Chris Green