In origin, this archaic word is linked to the heating water sense of boil rather than the bodily excrescence one. But the link is puzzling in one way because etymologists are still unsure what the gar- bit means or where it came from.
It’s ancient but according to the records it died out in British English dialect about a century ago. When it was around it meant a brawl, hubbub, hurly-burly or similar confused and noisy situation. It has been used by modern writers seeking a period flavour:
Then in ’82 there had been the Egyptian garboil I mentioned a moment ago.
Flashman and the Tiger, by George MacDonald Fraser, 1999. As the story is set in the nineteenth century, Harry Flashman means 1882, of course, the year of the Second Anglo-Egyptian War.
Its origin has been traced back through the Old French garbouille to Italian garbuglio, which in turn is from Latin bullire, to boil. Once you know that, the idea of a confrontation that boils into a tumult or fracas is easy enough to understand, even though we’re unsure why Italian added the gar- on the front. As a guess, it might have been to add emphasis rather than extend the sense.
The compound disgarboil once existed, meaning “disembowel”. It is long defunct — the Oxford English Dictionary has examples only from the sixteenth century. The meaning may well have been the result of a confusion with another ancient word, disgarbage, because the original sense of garbage was animal offal, often discarded as rubbish.