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AmazonThe fuse that protects this circuit is usually under the cowling of the outboard. Refer to your outboard's owner's manual for its exact location. If you find this fuse isn't blown, check for corrosion causing a bad connection and then see if you have power at the wire coming into the ignition switch.
The fuse feeding the key
On this boat the power to the key switch came through a fuse holder under the cowling. If that fuse blows, turning the key does absolutely nothing, because no power reaches the key to send back to the solenoid. It's the same symptom as a faulty neutral switch, so check both.