simple solenoid on your motor. Choke should only work with the key in the on position and pressed in. Simple adjustment move the solenoid body until it works correctly, And redo your wiring.
The fact you can hold those 2 spark plug wires means you do not have spark on those 2. . Is there water intrusion? those motors are known for exhaust gasket leaks. Timer base connected and moving ? Get an open air spark checker. make sure spark jumps 7/16 "
