I searched model 47044 and got zilch for parts list. So, you gotta wing it. Most all lawn tractor ignitions have 5 inputs:
B = Battery S = Starter solenoid M = Magneto (ignition coil module) G = Ground
and A = accessories (ignore this one)
You can find where the wires go and connect to the proper terminal on a universal ignition switch from an auto parts house or online.