From my personal experience, I finally decided the noun "gig" and the verb "to gig" comes from the synonym for laughing quietly'----GIGGLE.

Whenever I'd ask what the job paid, they would tell me and I would "GIGGLE". Then I'd walk the 35 miles to our shanty under a bridge and tell Carol what they had offered me to play 8 sets a night. She, too, would start to giggle ---- but not so quietly. The sounds soon took on a distinctly eerie and pathological tone. After about 20 minutes those squawkings turned into (morphed into) what always sounded like deep and heartwrenching sobs to my ears.

To this day I've never gotten over it.

Art Thieme