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