The legislative or governing body of every public agency having employees in positions covered by a retirement system who are ineligible to become members of such retirement system may in the case of any coverage group to which said agreement already applies, and upon the affirmative vote of a majority of the eligible employees in any coverage group of such public agency of which the employees who are ineligible to be members of such retirement system are a part, make formal application to the board for inclusion of the eligible employees of such coverage group in the said agreement; provided, that the terms of the agreement do not already apply to said positions; and provided, that on the effective date specified in said agreement relating to the coverage of such employees under the federal system, such employees are ineligible to be members of any retirement system.