Except as provided in any contract entered into by the council pursuant to City Charter Section 372, and subject to Sections 2.124.030 and 2.124.040 of this chapter, any person commencing employment with the city on or after the effective date of this chapter shall be a member of the Section 399 plan. Membership in this retirement plan shall be limited to full-time officers and employees of the city and, except as provided herein, shall not include persons employed by the city on a seasonal, limited-term, part-time or substitute basis, or elective officers or appointive members of city boards and commissions. The city council, by ordinance enacted by two-thirds of all members of the council, may authorize persons employed by the city on a seasonal, part-time or substitute basis to become members of this plan on such terms and conditions as it deems reasonable. (Prior code § 34.06.602)