I don't know EXACTLY which engine this is, I think it is a 407700. The reason why I don't know - the previous owner's mechanic took them literally when they stated they wanted flames, the mechanic left a fuel line loose and they got there wish. I replaced all the melted plastic and engine wiring harness. The original shroud was burned and I could not retrieve engine ID info. I purchased at auction all of the necessary replacement parts that I was told came from the same mower. Unfortunately, I needed the engine wiring harness and had to purchase that from a different person. The solenoid has two male square fork things inside a plastic rectangular receiver. The wiring harness plug for the solenoid I obtained has round females inside a rectangle with one side looking like a gable ended roof. Good news is the mower turns over, bad news is, it won't catch. After a few turns, the fuel pump began to leak gas out the weep holes. the carb is now flooded and drips gas onto the muffler. (if you got a match i can show you what a mower on fire looks like) I think the fuel shutoff solenoid is bad or the wiring harness to it isn't connecting properly. I have a plethora of questions. 1) how does one tell if the solenoid is working, should it "click" or some other giveaway ? 2) at what point should the fuel shutoff solenoid work - when you turn the key to on, or only when the motor is turning ? e.g - getting power via the alternator only ? 2a) could connect wires directly to the solenoid and test it that way to determine if wiring or solenoid problem ? 3) If I remove the Solenoid and install a plug, am I doing myself a disservice ? 4) If a deer farts in the woods in a calm day and you walk by five minutes later, would you recognize the smell ? ( I hope you had a nice winter Restrorob ) Once again, inquring minds want to know.