Turns out my first instinct about the key switch on the Cub Cadet 70 was exactly right, I pulled it out and found that the switch was grounding to its body.
Taking a look at the thing I noticed that the end cap where the electrical connections go was loose and tilted when they key turned. If I pushed the cap in everything was fine until I worked the key back and forth a couple times and the cap popped out again. Finally I pushed it in and peened the rim of the lock body over with a chisel, primitive but it worked.
Now the key supplies power to the coil the way it should.
While I was there I pulled the wire from the ammeter to the regulator, as I said yesterday this wire really wasn't doing anything. The last step (I hope) will be to move the grey wire from the hot side of the switch out to the ammeter. This should allow the ammeter to detect charge state while running. With luck I'll be able to use the ring terminal thats already on the grey wire without modification, as long as it will fit through the hole to the ammeter which is mounted on the right side of the steering pedestal.