Electric fuel pump recommendations?

I know fuel isn't getting to the carb because when it dies no fuel comes out of the carb into the bowls when I give it gas.
I'm sorry but that doesn't make sense. Maybe just the way it was written or maybe misunderstanding of how it works.
When it dies. Under what conditions does it die?
Giving it gas. Opening the throttle should result in fuel moving into the barrels from any combination of idle/transfer, booster, and shooters.
There must already be fuel in the bowl.
In many vapor lock situations, at closed throttle enough fuel makes it into the bowl to keep the engine running.

That filter could be a contributor.