Not more than one director shall be represented by such a deputy at any meeting or session of a board, commission, committee, or other governing body. Whenever, by any law, the director of any state department is made a member of a state board, commission, or committee, or of the governing body of any state agency or authority, the director may designate a deputy director of that department holding a position specified in subdivision (f) or (g) of Section 4 of Article VII of the California Constitution to act as such member in his or her place and stead, to all intents and purposes as though the director were personally present, including the right of the deputy to be counted in constituting a quorum, to participate in the proceedings of the board, commission, committee, or other governing body, and to vote upon any and all matters.