Paul's engine does not have the washer, and the parts list does not show one. Either I'm missing something, or Tecumseh missed something.
No, you had it right earlier. See the Engine Assembly section of the Tech Handbook.
I am forced to conclude that the references to the washer that I found in the tech manual, were for a different OHV engine.
Yep, the thrust washer is specific to two series of
horizontal shaft OHV engines, the OHH, and OHSK [models 50-70 only for the latter]. These have the MCR bobweight on the opposite side of the camgear to the cams.
This screenshot from a parts list for one of those, shows it a lot more clearly than the Tech HB.