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Basic operation is: Fuel in the bowl drains past a check valve into a passage at the bottom of the bowl, and fills the accelerator pump body. When you operate the throttle fairly quickly the pump leather pushes the fuel back into that passage. It can't reenter the bowl because of the check valve. Instead the other end of the passage turns upward toward the accelerator jet in the throat of the carb. There is a small valve in this vertical passage that also acts as a check valve of sorts. The fuel must be forced against it with enough pressure to raise it off its seat allowing the fuel to move up the passage to the jet.
First, when you operate the throttle, does the accelerator pump actually stroke? Second, is there fuel in the accelerator pump body? If there is fuel in the body and the pump strokes when you "blip" the throttle, but no fuel comes out the accelerator jet, there are only a few things that could be wrong.
If the inlet check valve is wasted the fuel gets pumped back into the bowl, and may or may not be pumped up the vertical passage to the jet. You can test the check valve by removing the bowl and blowing into the accelerator pump body. No air should come past the valve into the bowl bottom.
During this test you can also see if the passage to and past the pump valve is OK. Some air should move the pump valve off its seat and escape. If it doesn't then either the valve is stuck or the passage is plugged. If this is the case, shake the bowl. You should be able to hear a little tinnny rattle as the valve moves. If no rattle, then try soaking the float bowl in some carb cleaner.
Another problem might be the accelerator jet in the throat of the carb. I've seen these get clogged, and/or boogered up when some ham-hand tried to remove them. (I plead the Fifth!)
New bowls are available if yours is hosed. Used to see just the bowl check valves, but haven't in awhile. If the accelerator jet is messed up, you might try carefully turning it back & forth while applying upward force. That might allow it to be removed where you can see what is screwed up about it. I've fixed them in the past by redrilling the passages, but sometimes the process of removing them also enlarged the hole where they are pressed in. That, as you might guess, ain't good.
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