Jig, gigue is thread creep since these words have little to do with gig. Any supposed relationship between gigue and jig is speculative.

Jig (various spellings ) first appears in print in 1580. The OED observes that, its origin uncertain, it is "Often assumed to be identical with OF gigue, a kind of stringed instrument, a rude fiddle... but as to this there are difficulties: the OF word had none of the senses of jig, it was also obsolete long before jig is known to have existed..." [arguments presented here].
Jig has several meanings:
1. a lively, rapid, springy kind of dance. 1560.
2. the music for such a dance. 1588 (in Shakespeare).
3. A song or ballad of lively, jocular [etc.] character. 1570-1580. (Speaking of Scottish gigges or jigs- both spellings in the references of this date).
4. A lively performance, between acts or at the end of a play. 1592.
5. Jokes, jests, sport. 1592.
6. a name for various devices. 19th century.

Verb- some of its senses may have arisen differently from those of the noun.