http://man7.org/linux/man-pages/man8/pam_loginuid.8.html suggests that we should
use that for all "entry point"s for the user.  I guess we can add it.

Are you logging in using gdm?

We don't refer to pam_loginuid.so anywhere, so it's understandable that
/proc/self/loginuid is not set either.

Apparently, Ubuntu has the following:

/etc/pam.d/common-session-noninteractive:

session [default=1]                     pam_permit.so
session requisite                       pam_deny.so
session required                        pam_permit.so
session required        pam_unix.so 
session optional                        pam_winbind.so 
session required        pam_loginuid.so 

And then they @include the file above in /etc/pam.d/gdm