DK 35 SE pull coil/ engine stop solenoid

[Goodenough]

Or did I misunderstand that? Am I correct in thinking that if the starter solenoid clicks, the tractor cranks, the wire harness to engine shut-off solenoid reads 11.5 v (starting at 9.6v, increases after glow plug shuts off) with multimeter leads in red and black wire slots the solenoid should fire? What’s holding it back? Is the pull coil a separate piece?

 

[Goodenough]

If the photo above is the pull coil does anyone have a source for that part?