Not a clothing term, but a nautical one, from the sail whose name is probably a version of gibbet as it is suspended from the mast-head. It was in use as such by the 17th century but only 200 years later had the metaphorical slang spread beyond such circles - at much the same time as there was the East Anglian dialect for underlip. As for that pain of a builder, even worse than Fawlty Towers' Mr O'Reilly's, he was even less skilled than a gib - that is, one who disembowels fish.
AT LEAST the second builder turned up to give an estimate but immediately asked, "Insurance job, is it?" He was oblivious to the fact that such tacit jacking up of the price increases premiums for everybody. He will not get the work, but as a result I duly wondered about the cut of one's jib.