The fuel moving in the line shows that the carb wants to pump, but that the valve petals do not close well.
Thus it will only pump when the carb is all wet.
Get the fuel into the carb by closing the choke completely. If must be, close the small hole in the choke plate with a dab of solder.
Another reason may be, that the pump cover screw is too tight. This makes the valve petals curl up slightly. The screw should be loosely tightened.