Mounted on the side of the engine if it has one. Follow the fuel line as it goes to the pump. If the fuel line goes to the carburetor then it does not have a pump and is gravity fed.
Could be that the fuel pump clogged... or the diaphragm for the fuel pump commonly dies out.
They have an internal diaphragm that can rupture when it gets old.
There is only three reasons that a mechanical fuel pump will not pump fuel. The fuel filter maybe clogged and need replacement. It may also be the fuel pump diaphragm is busted requiring you to replace the fuel pump. You might be out of fuel.
The fuel pump diaphragm has broken. Needs new fuel pump.
Bad fuel pump diaphragm or excessive cranking with out starting . If it's alot look at fuel pump .
The arm of a mechanical fuel pump follows a cam and wherever the engine stops, that's where the fuel pump stops. The mechanical fuel pump is nothing more than a diaphragm with a couple "check valves" to force the fuel to only go in one direction. The diaphragm is spring loaded providing an effective pressure limitation.
Check fuel pump/filter. Sounds like pressure problem. If you are asking about a accelerator pump on a carburetor equipped engine then it is not spraying fuel either because there is no fuel available at the pump or the pump diaphragm is busted.
Some do and some don't. Some use gravity flow and some use a diaphragm type fuel pump.
A diaphragm inside that is moved back and forth normally by the crankshaft or cam.
Your engine likely has a diaphragm-type mechanical fuel pump. There may be a small crack in the diaphragm that is letting some air into the fuel line. You should replace the fuel pump before it leaves you stranded along the road.
I am guessing the pin being referred to is the fuel pump rod that rides on the cam lobe and creates the in and out motion required to activate the fuel pump lever that pushes on the diaphragm of the fuel pump to make it work.
If it is mechanical the diaphragm has a hole in it.