Under the council-manager form of local government, as proposed in the Town of Perdido’s draft charter, the town mayor is one of the council members and has no administrative authority (sometimes referred to as a “weak mayor”). They simply serve as the chairman of council meetings and sign documents and agreements on behalf of the council.
As laid out within the proposed municipal charter, the town council members are all elected by the citizens, and then the council members select from themselves who will run the meetings. The position of “weak mayor” is appointed.
Again, the title of mayor is primarily symbolic. If there were perhaps a holiday tree-lighting ceremony or 4th of July speech, the mayor would traditionally perform that duty. Beyond that and running town council meetings, the mayor has no administrative authority.