Get the kill tether with the 4 poles ...2 that are NO and 2 that are NC. Just splice it inline on the salmon wire before OEM kill button, attach to the NC terminals on new kill tether. This will break the ground from stator.
The primer only works if there is pressure in fuel system...either by bulb pumped up or by fuel pump when engine is cranked. To release pressure into carb/manifold fittings the key has to be pressed.
Cylinder can be damaged and still have good compression. A compression test only shows that a cylinder has enough pressure to support combustion but not the condition of engine. Rebuilt many a motor with good compression but bad cylinders
It is not a pump ..its a valve that opens with pushing in on keyswitch. The pressure in the fuel system and the cycles of the fuel pump is whats makes it "squirt"