From Clarence Major "Dictionary of Afro-American Slang", {New York, International Publishers, 1970, p.59}:
gig- "Originally a jazzman's job; later it came to mean any kind of job"

gig around- "working at any number of jobs"

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From: http://www.word-detective.com/back-n.html

"Gig," on the other hand, has remained in fairly constant use since it first appeared in its slang sense among jazz musicians in the mid-1920's. Meaning, as you say, a musician's "date" or engagement to play, "gig" is actually both a noun and a verb, though it's more common to hear a musician speak of "playing a gig" than "gigging." Though a "steady gig" is prized in the notoriously unpredictable life of a musician, the word itself carries overtones of the short-term "one-night stand." Reflecting its roots in jazz, "gig" is almost exclusively used by jazz, pop or rock musicians -- cellists play recitals or engagements, not "gigs."

Most dictionaries say that the origin of "gig" in this sense is unknown, but it really doesn't seem that great a mystery. Appearing in English in the 15th century, "gig" meant something that spins, as in "whirligig." Subsequent meanings included "joke," "merriment" and (aha!) "dance." Since playing at parties and dances is every musician's meal ticket early in their career, it's easy to see how "gig" became generalized to mean any paying job."

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And from http://www.wordorigins.org/wordorg.htm

"Gig is an interesting word with a variety of etymologically unrelated senses.

The oldest sense is that of a top or other whirling object. It dates to c. 1440. The origin is unknown. The sense of top is the source of some other senses, such as a giddy or flighty person, fun, merriment, and a whim.

The sense of a light, two-wheeled carriage dates to 1791. This sense is a transference from the earlier sense. The motion of the carriage and its tendency to upset are not unlike that of a top. Also related is the sense of gig meaning a ship's boat. This nautical sense dates to 1790.

Gig can also mean a spear or harpoon, and it is a verb meaning to spear or stab, as in Gig'em Aggies. This sense originally comes from the Spanish word for harpoon, fisga. The Spanish word appears in English in 1565 as fisgig. An alternate spelling is fizgig and the word is also folk-etymologized as fishgig, a harpoon for stabbing fish. The clipped form gig appears in 1722.

This brings us to the most common sense, that of a musician's engagement or job. The musical sense dates to 1926 and first arose as jazz slang in the US. But the origin is not in music. The use of gig to mean a non-musical job or occupation dates to 1908, and the sense of a business affair or event is a year older than that. The origin is unknown, but it may come from the slang term gag. This dates to 1890 and means business method, practice, or behavior. All these sense are American slang usages.

These last senses may be from, or be influenced by, an obsolete sense of gig. This sense of gig is a type of bet in a numbers game. It dates to 1847 and is an arbitrary use of the sense of gig as a carriage (a horse is another type of bet)".

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Best wishes,

Azizi