Did you check fuel at all three injectors? Your test would sort of indicate the pump but don't jump at it. Injector pumps are expensive. Stupid question I know, but I'll ask anyway, do you have the throttle wide open? If throttle is closed it won't pump. If the answer to that is yes and you are confident you have followed these bleed procedures Yanmar Tractor Fuel Bleeding Procedure then pulling the pump might the the next step.
I am still wondering about that "popping" sound. #2 on this camshaft drawing are the lobes that operated the injection pump. Certainly hope not and not suggesting it is your problem but just putting another possibility out there.
If you do get to the point of pulling the injector pump you will have to pull the little side inspection plate to give access to unhook the fuel rail from the governor. It is #7 on this drawing. Yanmar Tractor Parts: TIMING_COVER
I would encourage you to make several attempts at fuel filter and properly bleeding the system before moving to other possibilities.
I am still wondering about that "popping" sound. #2 on this camshaft drawing are the lobes that operated the injection pump. Certainly hope not and not suggesting it is your problem but just putting another possibility out there.
If you do get to the point of pulling the injector pump you will have to pull the little side inspection plate to give access to unhook the fuel rail from the governor. It is #7 on this drawing. Yanmar Tractor Parts: TIMING_COVER
I would encourage you to make several attempts at fuel filter and properly bleeding the system before moving to other possibilities.