Molerj is right, your engine does have a fuel pump. Looking at the flywheel, follow the fuel line coming from above the transmission onto the engine down until it ends at a square black plastic piece with another fitting that goes to a short piece of fuel line running to the carburetor. That small black plastic square is your fuel pump.
Since you say that overnight fuel returns to the filter, remove the cap from the fuel tank and try running it to see if the tank is causing pulling a vacuum on the line and keeping fuel from flowing. If that doesn't help, remove the fuel line at the filter and see if fuel will freely gravity feed out of the tank and into a container of some sort. Basically just to see if there is or isn't a blockage in the line or valve somewhere. If it flows freely and the tank isn't pulling a vacuum, then it's likely that your fuel pump is shot. Try hooking the inlet of the fuel pump or carb up to a gravity fed tank held just above the engine. If the engine runs fine without cutting out then your pump is definitely bad. If that's the case, you can:
1, buy a new pump from Kohler, for an M18 or M20 engine. They'll probably run you north of $100.
2, install a low pressure electric in place of the mechanical one and fabricate a block off plate where the old pump would've gone.
3, make a block off plate where the old mechanical pump would've gone and install a 1/4 hose fitting in the center of it. Connect a hose to the fitting and run the hose to the suction side of a standard Briggs vacuum pump for less that $20 and some time in the shop.
Rick
