2 Prong Semi Trailer Plug. For this to work, your outlet must have a center screw hole between the two plugs. Sometimes trying to plug a cord into a wall socket is like an adult version of that children's toy where you have to match the shapes up to get them to fit.
Two-prong outlets have no ground wire, without which the risk of electrocution and appliance damage is substantial. All B-Double and Semi Trailer + Drawbar Trailer Doubles are available with flatbed options for the semi trailer ONLY. If the compressor came as a two wire unit (not a three with the ground pin cut off) then yes you are good to go.
Most household extension cords only have two prong outlets.
Again, I'm not concerned with safety (I live dangerously).
In the North American market it is very common for brake lights and turn signals to be combined. Our dog chewed up one of our cord ends and I had to replace it. A number of standards prevail in North America, or parts of it, for trailer connectors, the electrical connectors between vehicles and the trailers they tow that provide a means of control for the trailers.