The terms you use are confusing. Cranking is what the starter motor does. It will "crank" whether or not the engine ever starts. The engine fires or starts, while cranking, when there is a spark and a combustible fuel/air mixture delivered to the cylinders. The U tube video shows a mechanical fuel pump with a perforated diaphragm and good seal on the internal shaft. This pushes the fuel from this perforation out of the vent hole. Fuel is still being pumped to the carburetor.
Heat soak of the engine, after being shut down, boils or percolates the fuel in the float bowl. This vaporized fuel fills the intake displacing the air/oxygen and delivering a mixture too rich to burn. Pumping the accelerator only further "floods" the engine not allowing it to start. To start a hot engine that's flooded just push the accelerator about 1/4 of a stroke and HOLD the pedal there. Now crank the engine to flush the excess fuel out. With air/oxygen in sufficient proportion to the fuel vapor, the cylinders will fire ie. the engine will start. There's no reason to diagnose this as a fuel pump problem. The owners manual of any carbureted vehicle describes the hot restart procedure.
Heat soak of the engine, after being shut down, boils or percolates the fuel in the float bowl. This vaporized fuel fills the intake displacing the air/oxygen and delivering a mixture too rich to burn. Pumping the accelerator only further "floods" the engine not allowing it to start. To start a hot engine that's flooded just push the accelerator about 1/4 of a stroke and HOLD the pedal there. Now crank the engine to flush the excess fuel out. With air/oxygen in sufficient proportion to the fuel vapor, the cylinders will fire ie. the engine will start. There's no reason to diagnose this as a fuel pump problem. The owners manual of any carbureted vehicle describes the hot restart procedure.