I have the Beitman's (1950, page 20) for the Admiral 20Y1 chassis, and I don't see a "osc/ shape coil". Inside a metal can there's a couple of coils for horiz frequency and horiz lock, on the plate of a 6SN7 horiz osc tube. Elsewhere there's horiz width and linearity, electronically near the flyback.
I may have the wrong diagram, though most Admirals of the time used similar circuits.