(a) General rule.--Council may appoint successors for vacancies on the board of health that occur:
(1) As five-year terms of board members expire. The successors shall serve for five-year terms.
(2) For any other reason, but a successor appointment shall be for the unexpired portion of the five-year term.
(b) Selection.--Successors, whether appointed for a five-year term or the unexpired portion of a five-year term, shall be selected from the members of the nonprofit corporation's board of directors.