JCubCadet: I've heard of 4-wire regulators with a terminal UNDERNEATH which I think went to ground. The earlier CC voltage regulators had a ground terminal on the opposite side of the case. Otherwise, I vote for a (former) connection to the headlight.
But, honestly, I think the only person who can answer the question, "Where does this wire go?" is you, you're the only one with the tractor in-hand. Roland Bedell is right, someone, at some point, is going to have to trace every wire down per the diagram, and hopefully label the wires as he/she goes.
If the battery is charged, but the tractor only runs when it is jumped, like Roland, I suspect an issue with the ground, and it may not be the wire you've pictured at all, it could be the negative battery terminal and/or wire from the negative post to the chassis.
It sounds like what is happening is that the vehicle or device which is doing the jumping may be supplying the reference (or ground) for the vehicle (tractor) being jumped. So when the ground is removed with the cable, there is no more 12 volts at the coil, and the motor dies. You need to be measuring 12 volts or more across the battery posts, AND from the chassis/frame to the positive post.
Do this: (1) measure voltage across the posts of the battery before you jump it. (2) measure voltage from the chassis to the positive post of the battery. If they're not the same, clean the ground connection at the frame until the readings are within 0.5 volts of each other (or better). Then (3) hook up the jumpers and make the same measurements. Next, (4) leave the meter hooked up from the frame to the positive post (or to the positive side of the ignition coil) when you crank it and while it is running. Finally, watch the meter closely when you remove the jumpers.
What you should see on the meter is around 12 volts with the motor off, and around 14 volts (13.6 or so) with the motor running and jumped, and the same (or similar reading) when the motor is running and not jumped (if you can get that far).
Again, from the sounds of it, you don't have any voltage from the frame to the positive side of the battery unless the tractor is being jumped.
Another "trick" you could try is running a wire directly from the negative side of the battery to the negative side of the coil, just to see if it will allow the tractor to run without being jumped and "prove" that it is a ground connection.
If the jumper wire from the negative post to the negative side of the coil doesn't work; disconnect both ends and try hooking the same wire up from the positive side of the coil to the positive post of the battery and crank it quick. If it works with the positive side of the coil hooked up to the battery, the problem is not the ground, but the key or something on the positive side.
Note: don't leave the wire hooked up from the battery to the positive side of the coil; it will drain your battery quickly if the points are closed while the motor is off --it is like leaving the key on.
I wish I lived closer to you, I wouldn't mind getting my hands on a 122.
Jeremiah