With this workaround in place, desktop wallpaper (on the working display) cannot be set using the ’Appearance’ configuration tool, and with automatic login the ’login screen as background’ effect (the image attached to #1) is there too. This could be Bug #1159430, and as mentioned there, I can work around it using Compiz’ Wallpaper plugin (i.e. setting a wallpaper in Compiz sets it on the external display).