Choke not working properly

I have a Briggs and Stratton 24HP 724CC Husqvarna riding mower. I can't get it to start when cold. The easiest way I can get it to start is to reach around the front a wiggle the choke lever that attaches up to the flap in the carburetor. It's not a choke cable issue. When the throttle is all the way up the choke lever is held in the up position. It won't start this way, only when I wiggle it slightly. Once running the engine starts fine and runs fine. I have noticed that if I engage the choke after starting it does not seem to cause the engine to run rough like you would expect if the choke is left on. I have removed the housing and checked all the connections and everything looks good and moves as I'd expect.