The feeling I get (since we're only speculating anyway) is that it would come from the word "gigue (zh-long e g) a dance, jig". I can hear a musician saying "I have a dance to do tonight" or " I have to go to a dance tonight" using the word gigue. "I have a gigue to do tonight" or "I have to go to a gigue tonight". I don't know. That seems to make sense.

Love, annap