The more I looks at this lathe, the more it reminds me of the combination Lathe/Mill machines; Clarke amongst others still sell something similar.
As I recall, some were available as a lathe only; Compare with one of the combos, as regards over-height tailstock, and spacer on the top slide, bed shape, lever or knob in the middle of the headstock, etc.
I’m not sure what’s being referred to here as a pull out knob, but the three position rotary knob on the front of the headstock, might be related to doubling the feed speed, rather than the spindle speed.
Have a look at this Grizzly manual, and you get the general idea; Page 22
https://cdn0.grizzly.com/manuals/g4015z_m.pdf
I’m guessing that the push/pull lever, is that gizmo on the centre of the V belt pulley.
Could it be something as simple as needing to position the knob on the from to the headstock on the correct place, and rotating the chuck by hand, to get some drive dogs to align?
Unlike the manual above, this only seems to have 2 pulleys, which don’t themselves slide, as per fig 15
Bill