It isn't a fuel problem but an ignition problem. When you push the throttle down you raise the pressure in the cylinder. More pressure takes a higher voltage spark to jump across the plug's gap. But you don't have enough voltage getting to the plug(s). And while there's no spark the gas is going down the exhaust. When you let up on the throttle the spark comes back and the hot exhaust gases ignite all the fuel that's gone down the exhaust system. (I learned about this at the age of three - in 1950 to be exact. I was standing by my father who was driving and I reached over and turned the key off. He immediately turned it back on, and it blew the muffler completely off.)

One possibility is bad plug wires. In that scenario the needed voltage goes through the sides of the wires to ground, and not through the plugs. Another is a bad rotor. Or a bad distributor cap. Or a bad coil. Or worn out plugs with a huge gap and dirty sides. But, probably not the ignition module as it usually fails completely.

I would replace what looks like it isn't new. A rotor and distributor cap might be first, followed by wires. Then maybe plugs. Or, do all of those if it hasn't had new ones in a while.