I was having fuel delivery problems on my 1998 Sportsman 500 and ended replacing float needle, needle seat, fuel lines and fuel shutoff. For a vacuum operated pump, you likely will not be able to blow through it without the vacuum pulse. The diaphragms in a pump are very thin and might have to be replaced if torn or old.
To narrow down the issue without jumping in and replacing everything, disconnect one line from tank at the shutoff and check for good flow, check both reserve and main fuel lines. Then reconnect and check for flow after shutoff turning switch to all 3 settings. Then make sure lines are all connected correctly and pull line that would go to carb and crank the engine over, it should be a good flow or pulsing flow or gas.
If it has not been done already, should figure on replacing needle and seat, fuel lines and fuel shutoff once running. My carb and shutoff allowed gas to overfill into brand new oil, which can damage engine if not drained, fixed and oil change.
Hope this helps!
Isaiah