You don't specifically say what carburetor you have but I think a stock 3a should have a Carter YF. I'm pretty sure accelerator pump diaphragm is only vacuum operated so pumping the gas pedal has no effect. Starting procedure is to pull the choke to create more vacuum and allow fuel to be pushed through the carb. Googling will give you plenty of information, whatever carb you have.
I agree with Lee, the diaphragms get stiff and crack. With ethanol fuel they only last a year or two. I would buy a new production rebuild kit and rebuild it yourself. It's not that hard if you take your time. There are YouTube videos to show you how. You really only need to replace the diaphragm, float valve and gaskets, although you can replace as much as you're comfortable with. And, very importantly check/set the float height. Buy a couple cans of carb cleaner and spray any and all orifices you can see. Add an inline fuel filter between the fuel tank and fuel pump. A switched inline fuel pump is also a convenient way to prime the system if it has been sitting a long time. Also, the kits come with parts for variations in models, you won't use them all.