That's not a choke solenoid. It is a primer solenoid. It is simply a valve. Pressing in on the key you should hear one click as the solenoid engages and maybe another when the key is released. With the key held in, fuel can pass through the solenoid actuated valve to enrichen the fuel mixture. You also need to squeeze the primer bulb until firm for first start of the day. After that this should not be necessary. And it was suggested you check the "kill" (man overboard switch) which is the lanyard you attach to yourself to kill the engine should you be pitched overboard. What you checked is the "ignition" switch.