I will be glad to try to help you with this issue. I just now saw your question as I have been offline for a few days.
The first thing is the safety switch diagram. I will have to research this and get it to you at a later time if you still need it after I give you the rest of the answer.
This issue that you are having is a fairly common problem. this is usually caused by the seat switch. It can be caused by a faulty switch or it can be caused by a bad connection on the switch.... or it can be caused by a broken wire or even a shorted sire in that area.
Check this out and you most likely will find your problem.
There are two different types of systems. I am not sure at this time which you have so I will describe them both.
One of the switch systems can be tested by just simply removing the wires from the switch and then seeing if the unit works. If this does not work, then you have the other, more common systems, this is tested by removing the wires from the safety switch and connecting a "Jumper wire" between the two wires. This will make a contact between the two wires and the unit should work. If this is the case, then you know that the problem is in the safety switch itself. Just replace the switch and you should be good to go.
The next question that you had was about the wire going to the bottom of the carburetor.
This wire is a positive electrical wire that feeds the fuel solenoid. This is actually what they call an "Afterfire" solenoid. It is designed to shit off the fuel to the engine when the ignition switch is turned off. When the ignition switch is turned on, electricity is applied to the solenoid which keeps it in the OPEN position. When the switch is turned off, it stops sending electricity to the solenoid and it shuts off the fuel. If there is NO electricity going to the fuel solenoid, the engine will not run. Sometimes these solenoids go bad and need replaced. Also they sometimes stop working because of a bad connection.
We DO NOT recommend that you eliminate this fuel solenoid because without it, you will get MASSIVE BACKFIRES that will BOW OUT the muffler and cause other engine damage.
I hope that this has helped you. Let me know if you still need the wiring diagrams and I will see if I can find it for you, but they are very difficult to find online.
I you want the information faster than I can find it for you, you can contact---- http://www.reynoldsfarmequipment.com/ and find their contact information. You should probably give them a call on the phone and they can get you these diagrams. I have worked with them for more than 30 years and they are good to work with.