A former state administrative official, after the termination of the official’s employment or term of office, shall not, for compensation, act as agent or attorney for, or otherwise represent, any other person (other than the State of California) before any court or state administrative agency or any officer or employee thereof by making any formal or informal appearance, or by making any oral or written communication with the intent to influence, in connection with any judicial, quasi-judicial, or other proceeding if both of the following apply:
(a) The State of California is a party or has a direct and substantial interest.
(b) The proceeding is one in which the former state administrative official participated.