Whenever by any provision of law an election is given to contracting agencies to subject themselves and their employees to provisions of this part otherwise not applicable to contracting agencies and their employees, and no other means of making the election is expressly provided, any contracting agency may make the election by amendment to its contract with the board approved in the manner provided for the approval of the contracts including an election among the employees affected unless the amendment only adds benefits without affecting members’ contributions, in which case the election among the employees is not required. An amendment to a joint contract that has been approved by the governing body of the county shall be deemed approved by the presiding officer of the trial court located within the county. The amendment shall specify the date upon which the agency and its employees shall become subject to the provisions. That date shall not be earlier than the first day following the approval of the contract pursuant to Section 20471, except that if the rate of the employer’s contributions changes, the effective date shall not be earlier than the first day of the pay period following the approval. Any election made by amendment to the contract shall be irrevocable until the contract is terminated. However, benefits provided by the amendment may be increased or improved from time to time by further amendment to the contract. From and after the date specified in the amendment to the contract the provisions, as they are in effect at the time of election and as they may be amended in the future, shall apply to the contracting agency and to its employees, and the rights, privileges, duties, liabilities, and responsibilities of the contracting agency and of each of its employees included in this system shall be governed thereby.