If the plunger dries out, then you don't get a good seal of the plunger in the bore nor the full shot of fuel into the venturi when you press on the accelerator. i.e. the fuel leaks back around the plunger instead of going into the venturi. Many of the plungers use what appears to be a piece of leather formed into a cup as the seal. When the leather dries out, it shrinks and never seems to go back to it's original size or flexibility.
Another problem could be a little sludge built up in the passage that feeds fuel from the bottom of the float bowl into the bottom of the accelerator pump well which could also be causing a fuel shortage.
When you quickly open the throttle, the intake manifold vacuum momentarily drops and the amount of fuel being pulled into the venturi drops correspondingly. The accelerator pump provides an extra shot of fuel to compensate for the loss of vacuum and prevents the mixture from leaning out. It's the lean mixture that causes the back fire.
(Sorry if the theory is old stuff to you!)
When I helped Teen48Flatbed overhaul his carb last spring, the little balls that go in several different places in the main body casting had been switched around. The ball that was supposed to be in the bottom of a small bore that fed fuel into the accelerator pump well (and serves as a check valve), had been switched with another one just slightly larger. End result was that the ball was jammed into the top of the bore rather than resting in the bottom and there was NO fuel getting to the accelerator pump. Ended up drilling a hole through the casting so I could drive ball out and then used JB Weld to fill the hole. The correct ball was made of aluminum instead of steel. That was just about the only way to tell the correct and incorrect balls apart. Only reference to the difference I found was in the factory service manual.
