carb manual ... when you look in the carb and pump, you should see a shot of liquid gas - the accelerator pump is for an extra shot under first load, otherwise generally speaking, the fuel route in is via jets that meter the flow depending on engine vacuum and throttle position, but requires the float bowl to be filled, which is controlled by the float opening and closing the inlet with a needle valve
starting and dying quickly probably means no fuel in the bowl, pop the top and look, might be a plugged inlet or stuck needle - and while it's open see if the accelerator pump looks deteriorated - if the carb hasn't had any attention in a long while, will be worth the time and few bucks rebuilding it
another check of the system is to remove the line at the carb inlet, poke it in a container and crank the engine to see if the pump is moving fuel well
Bill
