At its organization meeting, the Council shall elect one (1) of its members President of Council who shall preside at all of its meetings and shall have the power to vote. The President of Council shall be recognized as the head of the City government for all ceremonial purposes, but shall have no administrative duties. The President of Council and his successor, if any, shall serve until the next organization meeting unless he shall resign as President, or shall cease in the meantime to be a member of Council, or shall be removed by a vote of not less than two-thirds (2/3) of the members of Council, in which event Council shall proceed to elect a successor.