Help on Tillotson electric start

My Tillotson 212 electric start just clicks when I turn the key.
Bad battery? I jumper it from my (running) truck. Click.
Bad solenoid? I short the solenoid terminals, spark but it doesn't turn over.
The oil is full, so it's not likely the shutoff.
Can anyone help?
Is the solenoid mounted on the starter, or is the solenoid mounted somewhere else, with a cable going from the solenoid to the starter?

Did it ever start with the electric starter?
I bought this used, so I don't know if the starter ever worked, though I have to think it did or it would have been returned.

It's not the solenoid. I shorted the contacts and it still doesn't twitch.