What you are not seeing (and isn't detailed in the parts diagram, since individual parts are not available), is the lower half of the accelerator pump. There is a check ball for filling, and IIRC, one for squirting. The assembly is very small and delicate; If damaged, the factory can sell you a new bowl, which comes complete with those bits. Does the accelerator pump squirt (with fuel from the bowl) when you open the throttle? If not, it needs attention. Yes, the rubber boot is important. I have a couple on the shelf if you need one. It will test your dexterity and patience to change it, as you must disassemble/reassemble the throttle arm and associated return spring.
BTW, In order to do a proper soak, you must completely disassemble all parts, and soak them while disassembled... after a long soak in carb dip, we use a liberal dose of generic carb spray -- pushing the red tube of the aerosol directly onto passage openings, before reassembly, to dislodge any softened varnish crud. Often uses a whole can for one carb. Short of that, you may well still have some varnishing.
Note: If there is any evidence of white aluminum oxide corrosion, you may need another carb, as you can'y dissolve that with carb dip.
