This archetypal American word derives from the Algonquian dialect of Native Americans in Massachusetts. In their language, it meant “war leader”. The Puritan missionary John Eliot used it in his translation of the Bible into their language in 1663 to convey the English words duke, officer and captain.
Mugwump was brought into English in the early nineteenth century as a humorous term for a boss, bigwig, grand panjandrum, or other person in authority, although often one of a minor and inconsequential sort. This example comes from a story in an 1867 issue of Atlantic Monthly: “I’ve got one of your gang in irons — the Great Mugwump himself, I reckon — strongly guarded by men armed to the teeth; so you just ride up here and surrender”.
It hit the big time in 1884, during the presidential election that set Grover Cleveland against the Republican James G Blaine. Some Republicans refused to support Blaine, changed sides, and the New York Sun labelled them little mugwumps. Almost overnight, the sense of the word changed to turncoat. Later, it came to mean a politician who either could not or would not make up his mind on some important issue, or who refused to take a stand when he was expected to do so. Hence the old joke that a mugwump is a person sitting on the fence, with his mug on one side and his wump on the other.
There is also a slangy sense — less known these days, I believe — of a person who has been persuaded by his possession of a minor official position into a sense of self-importance, often becoming obnoxious as a result.