There shall be a city manager. The council shall appoint him or her for an indefinite term by a vote of a majority of all its members. It shall choose him or her solely on the basis of his or her executive and administrative qualifications. At the time of his or her appointment, he or she need not be a resident of the city or state; but, during his or her tenure of office, he or she shall reside within the city. Neither the mayor nor any other council member may be appointed city manager during the term for which he or she shall have been elected nor within two (2) years after the expiration of his or her term. The council may suspend or remove the city manager at any time by a vote of a majority of all its members.