Sec. 10. This section applies to the appointment of members to the library board of a public library serving a library district that is located in more than one (1) county and is not entirely located within the boundaries of one (1) municipality. For a public library under this section, the appointments under section 9(4) and 9(5) of this chapter shall be made as follows:
(1) One (1) member appointed jointly by the executive of the respective counties.
(2) One (1) member appointed jointly by the fiscal bodies of the respective counties.