My experience is that the pump does not need bleeding in this situation or any situation, it’s self priming and will pick up fuel fast.
Just for sanity check, open the gas cap when you try to crank it over with known good fuel level in the tank.
If no gas is leaking out the drain hole under the pump the main diaphragm isn’t shot
And if the pump isn’t working but not leaking that means it might just need a thorough cleaning to work again
The check valves in the pump rarely go bad they just need to be cleaned most of the time.
The cam arm might be worn out or broken but that’s easy to fix compared to the rest of it, assuming you are not shy with the welder
If I was you I would just take the pump out and break it down on the bench
Thorough inspect and clean all parts and reassemble it
That way you know it’s good.
-s
