At this point is would help us if we had the Briggs model number information from the engine so we can check the parts diagrams and other sources to determine what setup your engine has. Briggs has several different versions depending on the engine.
But is a quick rundown. When the engine starts air from the rotating fan attached to the flywheel pushes the choke air vane away from the flywheel. the vane is connected to the choke shaft via either a linkage or in some setups the end of the vane has a hanging pin that sits in a notch on the choke shaft that rotates the choke to the open position.