In the event that the position of Constable becomes vacant,
whether it be due to death, resignation, or some other incapacity,
the Mayor shall appoint a new Constable to fill the position for the
remainder of the term up to the next regular Town election, provided
that when the vacating Constable shall have been elected as a member
of a political party, such vacancy shall be filled by the appointment
of a person of the same political party.