gnome-session-quit --logout --no-prompt
And if those two files are empty then logging is not set for lightdm and greeter.
Open gnome-system-log, keep it open
at some point it will hang, note time and the line. (bold text)
Next time post the log and check if there are other logs after that line. Though I believe if syslog service itself stops, it won’t show the log, in that case you have to use journalctl.