Section 59E. In any city which has accepted sections fifty-nine B to fifty-nine D, inclusive, and accepts this section, and in any city or town which has a reserve force of firemen under authority of special law and accepts this section, no person shall, after the date of acceptance of this section, be appointed to the reserve force of firemen thereof unless appointments to such force are subject to chapter thirty-one and the name of such person shall have been placed, on or before said date, on an eligible list established under said chapter and the rules made thereunder for such appointments.