The governing body of the library capital facility area shall be three members of the county legislative authority from each county in which the library capital facility area is located. In counties that have more than three members of their legislative body, the three members who shall serve on the governing body of the library capital facility area shall be chosen by the full membership of the county legislative authority. Where the library capital facility area is located in more than one county, a county may be represented by less than three members by mutual agreement of the legislative authorities of the participating counties.