First, check that the fuel tank cap vent holes are not clogged. Probe into any holes you see in the cap (outside of cap & inside too).
Testing the pump is done by disconnecting the hose that runs from pump to carb (take loose at carb), then insert the open end of hose into a plastic soda bottle. Crank the engine and you should see good spurts of fuel being delivered to the bottle every time the pump operates.
But, if the tank cap vent is clogged, the pump can't deliver fuel. So make certain the cap is venting first. If it is not apparent whether the cap is clogged or not, try running or testing pump with the cap removed, or at least "loose".

99 year model is way over due for fuel hose replacement? have you even don that? Look for weather cracked/rotted fuel lines? Usually you will see some wettness, if so these are about to go and my burn you LT to the ground.

I if the weather cracks or rot alows sucking of any air it won't pull the gas up to the pump or pass it. This would also be an fire issue if the hoses looked weather cracked at the carb. and around the engine. Check them all the way back to the fuel tank.

Also most old kohlers have a diaphramn fuel pump lever that runs off a camshaft just like the old SBC and Fords designs. is so you should be about to test the pump by actuating the lever and hear the air or put two hoses on it and dip one in a glass full of liquid and it should pump it out the other end.