I have heard people say, "It's your gig" when they intend to say, "It's your choice after all." For example:
I have said all I wanted to say. Now it's your gig.
The intention is that the listener is the one who has to decide then.
What does "gig" mean here? Gig seems to have multiple meanings in dictionaries but I am unable to find what fits well in this phrase. Also, does "It's your gig" have any history or specific etymology?