I'm having a problem visualizing your setup ... what I'm picturing is 4 wire columns with coals in them mounted vertically arranged in some pattern around a tripod from which is suspended a turkey, probably also hanging vertically, and you put some aluminum foil around some part of it somewhere?
It sounds like a version of a vertical grill/broiler, like they use to make gyros, if I'm picturing this right.
A 12 to 14 pound turkey may take from 4 to 5 hours - more or less time. There are so many variables. If you doing this outdoors, how cold, warm or windy is it? How hot is your fire? How far from the heat is the meat? How fast is the rotisserie turning? How is the foil being used? Is it trapping in heat to turn this into more of an oven?
"It ain't what you don't know that gets you in trouble. It's what you know for sure that just ain't so." - Mark Twain