Whenever a member of an elected board of trustees of a fire protection district ceases to be an inhabitant of the district, his or her office shall become immediately vacant. Whenever a vacancy in the board of trustees occurs, either by death, resignation, refusal to qualify, ceasing to be an inhabitant of the district, or for any other reason, the vacancy shall be filled as follows: (i) if the vacancy is in a 3-member, 5-member, or 7-member appointed board, by the appropriate appointing authority, and (ii) if the vacancy is in an elected board, by the elected board within 60 days after the vacancy occurs. The person appointed shall qualify for office as provided in this Act and shall thereupon assume the duties of the office for the unexpired term to which the person was appointed, except that in a district in which trustees are elected, the person appointed to fill a vacancy shall serve only until the first Monday of the month following the month of the next regular election, and at that election a trustee shall be elected to fill the vacancy for any balance of the unexpired term and until the elected trustee has qualified.