Tada! (insert trumpet fanfare here.) I got it working.
Wouldn't you know, though, the only guage of stranded wire I don't have is 12. I went ahead with a 3" length of 10 guage stranded wire. I had a spare eyelet that fit over the small post and I stripped an inch and a half of the other end and wrapped it around the mounting stud and "smushed" it between the solenoid and the mount. As I was putting it all together I realized that I left my emery paper a long 10 yard walk away in the garge, so I just scraped of some rust with a screwdriver and snugged the bolt down tight.
Now for the rest of the story...
Solenoid worked great the first time I tried it, however after that the switch quit working. I verified this with the test light. Whereas before I got power from the switch to ground when I turned the key, I was getting nothing from switch to ground last night.
Here's my theory. Whoever had the tractor before knew the solenoid was bad so he just jumpered it everytime he started it. Therefore the contact points inside the switch weren't used often enough and some corrosion built up. When I finally got the solenoid working, there was enough contact to run the starter the first few times, but due to a poor connection there was some arcing and the connection went bad. (I have nothing to back this up, but it makes a good story.)
I filled the switch with WD-40 and ran it back and forth a hundred times or so. I shook it, tapped on it, called it a few names, and then plugged it back in. Tried it 3 or 4 times and it worked every time.
Stay with me here...The story continues...
So, I put the choke on and started up the tractor. The thing really does purr like a kitten. For all that is wrong with this tractor, the guy must have taken pretty good care of the engine. I ran it for a few minutes and then turned the key to shut it off. Now the key won't shut it off. It just kept on running. I shorted the plug to ground to kill the engine and tried again a few times. I had to short the plug to shut it off every time. By this time it's 11:30 at night. So, I packed up and went to bed.
I'll have to try again tonight when I get home to see if letting the WD-40 dissipate helps. I suspect also that I may have move some wires around on the connector that plugs into the switch and created a short that continues to allow current to the ignition even after it's switched off.