Two or more members of the governing body of a political subdivision may perform a duty placed by this code on the presiding officer of the governing body if the office is vacant or the presiding officer fails to perform the duty unless:
(1) a single member of the governing body designated by law to act in place of the presiding officer performs the duty; or
(2) this code specifies that the duty is to be performed by another authority acting in place of the presiding officer.