My pal Kenny has that same tractor.
It's a honey of a machine.
I don't know all the ins and outs on it but have used it some.
On his that's how the throttle handle is supposed to work - push it all the way forward to kill the engine. There are no electrical connections to the injector pump on those tractors. The fuel system is entirely mechanical.
You could start the engine then take the battery out and the engine would run fine all day untill you shut it off with the handle. Or you could park it on a hill and roll start it. Won't hurt anything.
I think the button you are pointing to operates the air preheaters. There are two big spark plug looking things in the intake manifold that heat up the air. It is a cold weather starting aid. Push the button and you should hear a solenoid click if the system is working. There is a very good Ford specific forum here at Yesterday's Tractors with a very knowledgeable bunch of fellows there.
Click on the link below if you have more questions about your tractor.