(a) The following definitions shall apply for purposes of this section:

1. (1) “Board of supervisors” means the Board of Supervisors of the County of Contra Costa.
2. (2) “County” means the County of Contra Costa.
3. (3) “District” means the West Contra Costa Healthcare District.
4. (4) “District board” means the board of directors of the West Contra Costa Healthcare District.

(c)

1. (1) If the board of supervisors elects not to serve as the district board pursuant to subdivision (b), it shall appoint a district board consisting of five members, all of whom shall reside in the district. The members appointed by the board may include, but need not be limited to, at least one of each of the following:

   1. (A) A county supervisor.
   2. (B) A city council member of any city located within district boundaries.
2. (2) The term of a district board member appointed under this subdivision shall be for four years, or until his or her successor qualifies and takes office.
3. (3) The board of supervisors shall determine whether members of the district board shall serve at the pleasure of the board of supervisors, or for staggered four-year terms, subject to removal for cause. Vacancies shall be filled by appointment of the board of supervisors.