Tim
The info provided by Whitetiger is most helpful.
It confirms there are two independent coils inside the stop solenoid.
The coils need to be tested following the procedure below.
Each terminal on the electrical connector needs to have its resistance to the solenoid case measured.
The coils have significantly different resistance values.
I know you said there is no power in the start position but it is important we verify that both coils within the solenoid are OK.
The power for the solenoid, which I have marked with a blue line, comes from the battery with no fuse.
The solenoid power first flows to a relay shown as #11.
The relay trigger control is marked with a red line.
The key switch #2 has a number of circles within boxes.
This is telling you which terminals of the switch are connected at different switch positions.
The relay trigger wire is connected to the AC or ON position of the switch so the engine stop relay should be powered with the key ON.
The same trigger wire becomes connected to the power in the switch in the start position.
If as you have stated the power supply to the solenoid disappears in the key START position then the key switch becomes suspect.
However, please check the solenoid coils first.
I have attached WSM pages dealing with checking the key switch.
Dave