Once I've make my shapes, flowers, etc., how long does it take for the gumpaste to harden to the point where it will stand upright? I'm making a rainbow that will span from one cake to another.
It depends on the thickness when I make wired flowers if I do not let them dry for several days they will break where it is thicker next to the wire. and flowers are very thin
I would hazard a guess anything large enough to span between two cakes would need a couple of weeks.... I would also put some sort of support inside it.
This might be a great time to use a Duff trick and make it out of styrofoam covered with fondant.
It depends on how warm. humid etc it is and as msmeg said, how thick and big. Also depends on the recipe you are using. Drying it on a bed of cornstarch helps hasten things. I still would give it 3-7 days, but most of the time overnight has worked for me.