To me the pertinent bit is
(time and circumstance permitting) and, whenever possible, should be passed in the order given
When I teach EFATO I tell the student that if he just gets his callsign and "Mayday" out (assuming some sort of ground radio station) then that is enough, the guy on the radio should know that an aircraft with that callsign has just taken off and if there is a Mayday at that point know roughly where you are and you are in trouble.