Hello,
thanks for maintaining greetd on Debian :)

(this is roughly the equivalent of #1023982, for sysvinit and other
 inits that use the DEFAULT_DISPLAY_MANAGER variable like runit)
while testing the sysvinit script I noticed that it checks for
$DEFAULT_DISPLAY_MANAGER (like each other sysv script for a display
manager in Debian) but there is no debconf question on install that
asks for the default default display manager.

As a result:
if greetd is the only one/first display manager installed on the
system the /etc/X11/default-display-manager file is not found and greetd
starts;
if another display manager is/was installed, /etc/X11/default-display-manager
file is found and is either empty or has the path for another display manager
and greetd is not started.
The workaround is to echo /usr/sbin/greetd  > /etc/X11/default-display-manager
but that is not how this mechanism is supposed to work; for comparison other
display manager have a debconf question on install that ask for the desired default
dm among a list (and writes the path in the file).

this is a mechanism intended to prevent the start of two dm at the same time.
I don't have a proper patch, but I think roughly:

* add a dependency on debconf (>=0.5) | debconf-2.0
* add a template, debian/greetd.templates (just copy the one from
  lightdm or sddm, changing the name and path to greetd)
* add code to handle the debconf question in postinst
* add code to for debconf to remove greetd from the list of
  available dm in prerm

all other dm handle this in a similar way, I'm attaching lightdm
postinst and prerm debconf snippets as example

Thanks,
Lorenzo
---postinst---

THIS_PACKAGE=lightdm #NOTE should be changed to greetd
DEFAULT_DISPLAY_MANAGER_FILE=/etc/X11/default-display-manager

# debconf is not a registry, so we only fiddle with the default file if it
# does not exist
if [ ! -e "$DEFAULT_DISPLAY_MANAGER_FILE" ]; then
  if db_get shared/default-x-display-manager; then
    # workaround debconf passthru bug (#379198)
    if [ -z "$RET" ]; then
      $RET="$THIS_PACKAGE"
    fi
    if [ "$THIS_PACKAGE" != "$RET" ]; then
      echo "Please be sure to run \"dpkg --configure $RET\"."
    fi
    if db_get "$RET"/daemon_name; then
      echo "$RET" > $DEFAULT_DISPLAY_MANAGER_FILE
    fi
  fi
fi

# remove the displaced old default display manager file if it exists
if [ -e "$DEFAULT_DISPLAY_MANAGER_FILE.dpkg-tmp" ]; then
  rm "$DEFAULT_DISPLAY_MANAGER_FILE.dpkg-tmp"
fi

# debconf hangs if lightdm gets started below without this
db_stop || true

----------

---prerm---

THIS_PACKAGE=lightdm  #NOTE should be changed to greetd
DEFAULT_DISPLAY_MANAGER_FILE=/etc/X11/default-display-manager

if [ "$1" = "remove" -o "$1" = "deconfigure" ]; then
  if [ -e /usr/share/debconf/confmodule ]; then
    . /usr/share/debconf/confmodule
    # disown this question
    db_unregister shared/default-x-display-manager || true
    # does the question still exist?
    if db_get shared/default-x-display-manager; then
      db_metaget shared/default-x-display-manager owners
      db_subst shared/default-x-display-manager choices "$RET"
      db_get shared/default-x-display-manager
      # are we removing the currently selected display manager?
      if [ "$THIS_PACKAGE" = "$RET" ]; then
        if [ -e "$DEFAULT_DISPLAY_MANAGER_FILE" ]; then
          db_get "$RET"/daemon_name
          if [ "$(cat $DEFAULT_DISPLAY_MANAGER_FILE)" = "$RET" ]; then
            rm "$DEFAULT_DISPLAY_MANAGER_FILE"
          fi
        fi
        # ask the user to choose a new default
        db_fset shared/default-x-display-manager seen false
        db_input critical shared/default-x-display-manager || true
        db_go
        # if the display manager file doesn't exist, write it with the path
        # to the new default display manager
        if [ ! -e $DEFAULT_DISPLAY_MANAGER_FILE ]; then
          db_get shared/default-x-display-manager
          echo "Please be sure to run \"dpkg-reconfigure $RET\"."
          db_get "$RET"/daemon_name
          echo "$RET" > "$DEFAULT_DISPLAY_MANAGER_FILE"
        fi
      fi
    fi
  fi
fi

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