Yes, you should be able to get multiple squirts from pumping, not just 1 1/2 pumps.
You might have a leaky bowl, meaning fuel could be leaking into the engine when setting.
You might have fuel perculation. With the formulation of fuel nowadays, it could be evaporating after engine shut-off. This more pronounced during the summer months, hot temperature.
You can check fuel level by removing the air cleaner and sticking a pipe cleaner down the vent, large 1/4 inch diameter tube sticking up in the middle of the carb, right after shut down and before startup to compare fuel level.
It could be formation again by maybe the fuel "icing" the squirter. If wrong recipe used for the area used in, fuel would freeze in the squirter. I've had this happen to me in the past. Gas pedal became really hard to push when squirter froze.
Or, the check ball at the inlet, bottom of the well, for accelerator piston maybe missing or the ball or seat may have a defect in the seat not allowing a good shutoff of fuel when piston goes down in its cylinder to push fuel out the sqirter.
Before startup, you might remove the air cleaner and open the throttle plates wide open and view with a flashlight to see in intake floor is wet. If it is, carb is leaking.
Others here will have some good suggestions....
Everett "OBJECTS IN THE MIRROR APPEAR QUICKLY UPON RAPID DECELERATION"