Check for spark. The coils are hard to find. There are alternatives tho.
Follow the fuel line. Mine screws into the carb intake. It is rectangular(1"x 2 1/2" x 1/2") and gaskets should be available. If not, I could send you a used fuel pump. I would need to check diagrams to make sure they are the same.
Generally, the fuel pump will be between the carb and gas tank but closer to the engine so it can use the vaccuum from the engine.
If you blew air from the fuel line to the tank, you might have ruffled the gasket inside the fuel pump. Make sure float is moving freely.
I think mostly 10hp up engines use fuel pumps. There is a way to install a fuel pump that runs off of vaccuum if you need to.