This is why you need the parts book for both the engine & the mower.
Fuel pumps are generally only fitted to engines on mowers where the fuel tank is lower than the carburettor float bowl.
Usually these mowers have the fuel tank under the seat or rear guards.
Your mower has the tank under the dash so the fuel will flow by gravity alone to the carb.
So I'm back to square one having no idea what the problem is. Awesome. Time to pay someone with more brains than me.