(1) In the exercise by the board of directors of its authority in respect to the filling of vacancies in executive positions and memberships on municipal boards, authorities, and commissions, only those qualified electors of the city found by the directors to possess the necessary qualifications shall be appointed or confirmed.
(2) Provided, a board of directors may appoint, at its discretion, persons who reside outside the city to museum boards and commissions.
(3) In filling vacancies on any municipal board, authority, or commission, unless the statute applicable to the position forbids the appointment thereto of a city employee, the city manager, if otherwise qualified, shall be an eligible appointee.
(4) The city manager, however, shall not be, ex officio, a member of any municipal board, authority, or commission.