No, it does not have to be another citizen. Exactly three conditions need to be fulfilled for one to be able to become mayor of a town:
The town currently has no mayor
The character trying to become mayor has Compacts & Constitutions
Either the character trying to become mayor needs to be a citizen of the town, or the town must be out of authority, or there must be no citizens at all in the town.
If you right-click the townbell without getting the option to become mayor, that means at least one of the above is not true.
I appreciate the quick responses. Everyone has now left the town (was 2 of us). Now when we goto click the town bell it gives us the message "This land is owned by xxxxxx" now.
“Do not rely on a rabbit's foot for luck, after all, it didn't work out too well for the rabbit.”