The term of office of judges of any separate juvenile court, who are approved by the electorate, shall be for six years beginning on the first Thursday after the first Tuesday in January following his or her approval by the electorate. Any judge of any separate juvenile court appointed to office after the expiration of the term of incumbent judges shall serve for three full years after his or her appointment and thereafter, if he or she desires to continue in office, shall cause his or her right to continue in office to be submitted to the electorate in the manner provided by law at the first general election held after he or she has served three full years as such judge, and the term of office for which he or she was appointed shall expire on the first Thursday after the first Tuesday of January following the general election at which his or her right to continue in office was subject to approval of the electorate.