"Mugwump" is rarely used today; if it is used, it's usually in a humorous or an historical context.
(Oxford English Dictionary)
mugwump, n. and a.
Chiefly N. Amer.
[< Massachusett mugquomp (also in form mummugquomp) war leader (1663 in Eliot's Massachusett Bible, freq. translating 'officer', 'captain', and 'duke').
There is no reason to believe that this is an old borrowing unattested before the 19th-cent. humorous use. It may perhaps originally have been used in mockery of the titles of rank in some mason-like societies; see quot. 1832 and cf.:
1835 D. P. THOMPSON Adventures Timothy Peacock i. 6 This village, I beg leave to introduce to the reader, under the significant appellation of Mugwump, a word which being duly interpreted means..much the same as Mah-hah-bonewhich last,..I have fortunately discovered to signify nothing in particular; though..I am aware that both these terms are used vulgarly and masonically, as synonymous with greatness and strength.
Perhaps cf. also SACHEM n.]
1. orig. and chiefly humorous. An important person, a leader, a boss.
1832 in Nation (1891) 21 May 414/3 It has extensively circulated among the Knights of Kadosh and the Most Worshipful Mugwumps of the Cabletow. 1877 N.Y. Tribune 16 Feb. 4/4, John A. Logan is the Head Center, the Hub, the King Pin, the Main Spring, Mogul, and Mugwump of the final plot.
2. a. A person who remains aloof from party politics, professing political disinterest; (U.S. Hist.) a Republican who in 1884 refused to support the Republican party nominee for president. Also: a person who changes political parties, esp. with a view to personal advancement.
1884 Sun (N.Y.) 23 Mar. 1/5 (headline) Mugwump Bradley wins. 1884 Sat. Rev. 22 Nov. 659/1 It may be that in a few years..a little group of British Mugwumps..will arise. 1898 Academy 22 Oct. 109 Halifax is, of course, the typical 'trimmer', which is to say 'mugwump' of Restoration politics.
b. In extended use (usu. somewhat derogatory): a person who remains neutral or non-committal; an aloof, independent, or self-important person. In quot. 1887 applied to an animal.
1887 J. D. BILLINGS Hardtack & Coffee xv. 286 [The mule's] reputation as a kicker is world-wide. He was the Mugwump of the service.
17 February 1877, Williamsport (PA) Daily Gazette and Bulletin, pg. 2, col. 2:
As Tilden is lost the Tribune recommends that the Democrats should immediately proceed to impeach Logan. It says: "John A. Logan is the head centre, the Hub, the King Pin, the Main Spring, Mogul and Mugwump of the final plot by which partisanship was installed in the commission."
26 March 1884, Boston Daily Globe, pg. 4::
Somebody having expressed a desire to know what in the world a mugwump is, the New York Sun sheds the light of its knowledge upon the question with the following effect: "A mugwump, in the cherished vocabulary of the New England States, is a big person; big not necessarily in frame, or voice, or in the pugilistic prowess of our later Boston, not always big in brain or sense, but big somehow. A little man in a big place and not yet found out is a mugwump, but so is a big man in a big place. One may be a mugwump because his father was, or he may become one by marrying a mugwump's child. If he is a descendant of the great mugwump Elder BREWSTED, or of the greater mugwump Governor WILLIAM BRADFORD or of the moderately great Connecticut mugwump General JOHN MASON, who killed off the Pequots, he is likely to be a mugwump all his life. If he is only General BUTLER and is elected governor he is a mugwump pro tem. The faculty of Hardward College and, possibly, of Yale College are decidedly mugwumpish, if we may coin the word, in the towns which they inhabit. The mugwump, in short, is one of the big toads in the puddle, and sizes and qualities vary with the puddles."