Section 112A. A veteran, as defined in section one of chapter thirty-one, who holds in the service of a city which accepts this section by vote of its city council, subject to the provisions of its charter, or of a town which accepts the same by vote of its inhabitants at a town meeting, an office or position not classified under said chapter thirty-one, other than an elective office, an appointive office for a fixed term or the offices of city solicitor, assistant city solicitor, secretary to the mayor, clerk of the board of selectmen, town counsel, assistant town counsel, legislative counsel, registrars of voters or other officers performing similar duties, or public school teachers, and has held such office or position for not less than five years, shall not be involuntarily separated from such office or position except subject to and in accordance with the provisions of sections forty-one to forty-five, inclusive, of said chapter thirty-one to the same extent as if said office or position were classified under said chapter. If the separation in the case of any such unclassified office or position results from lack of work or lack of money, such a veteran shall not be separated from his office or position while similar offices or positions in the same group or grade exist unless all such offices or positions are held by such veterans, in which case such separation shall occur in the inverse order of their respective original appointments.