Mugwump is a term that came into wide use in the later 19th century. Without getting into detail, it had to do with rejecting the GOP and corruption and becoming independent. My Dad, part of what had been a staunch New England Republican family rejected the party during the 2nd half of the Reagan era. For reasons no one seems to remember, he was referred to as Mugwump the elder and I, in turn, became Mugwump the younger.
IOW, I take the Groucho Marx approach to party affiliation.