Any emergency medical service district created pursuant to this chapter shall be administered in one of the following manners:
The governing authorities of the participating political subdivisions shall appoint a person or persons, who may be an elected official of such political subdivision, to a board which shall be authorized to promulgate policy for and guide the administration of the activities of the district; or
The governing authorities, by mutual and unanimous agreement, shall appoint an executive manager who shall have full authority over the operation of the district.