What year is your engine? Older carb’d engines had an extra set of butterflies , choke flappers, that would close when you push in on the key to choke the engine. On most OMC’s these had an electric solenoid that would pull the butterflies closed then open when you let off the key.
Later models used a primer solenoid which would squirt extra fuel in the intake. This also required the operator to push in on the key or hit a choke button to engage the solenoid.
So, do you have 2 sets of butterflies in your carbs or do you see a small black solenoid with a red arrow handle on it. If you see the red arrow you have a primer solenoid. Figuring out which you have will help.