I am having the same problem on my 53 GMC. The brakes are more like the ones described in the older manual https://chevy.oldcarmanualproject.com/shop/1948_51truck/index.htm

Reading carefully, the manual instructs you to loosen the top brake adjuster on both rear wheels. This allows the piston to retract downward to help remove the air pocket / space above the bleeder screw opening inside the wheel cylinder. Bleed the brakes as normal, then adjust the upper adjuster back to its operating position. This makes sense, however I just performed this procedure and no luck. Still needs a pump of the pedal before getting any braking. On my truck, I am confident the issue is in the rear because I have plugged off the rear and the pedal is rock hard (no pumping).

This has been very frustrating.