All employees who have acquired permanent status shall, subject to this part, have permanent status in their present positions so long as such positions remain in the classified service. All other employees shall be eligible to acquire permanent status in their present positions so long as such positions remain in the classified service in the manner provided in Section 45-35-120.13, upon completing six months’ service in such positions, such time to be computed from the beginning of such service, rather than from May 30, 1984.