Good morning and sorry for the delay. We all do this on the side, out of our houses. When you had replied back last night I was out for the evening.
On this engine the fuel pump is also the oil pump. The pump serves 2 functions, it draws fuel from the fuel tank, and also draws oil from the oil tank, and then it mixes the fuel and oil inside of the pump before sending it out to the carburetors.
When the no oil warning comes on, it can mean a couple of things
1. There is a hose that connects the fuel pump to the engine block. This is called a pulser hose. If that hose is loose, torn, or compromised, the pump will not cycle correctly, and will not draw enough oil from the oil tank
2. There is a fuel line between the fuel pump and fuel tank. When the engine is running, the fuel line is always under a vacuum (the pump "sucks" fuel up from the tank). If there is any kind of air/vacuum leak on the fuel line, the pump will draw air in through that leak. This will again cause the pump not to cycle correctly, and not draw enough oil from the tank.
3. There is an oil line between the pump and oil tank. If the line has collapsed internally or is pinched, that will cause a lack of oil to the pump
4. In the oil tank itself is a strainer type filter, if that is clogged up that will cause the a lack of oil to the pump as well.
5. Lastly, if the pump is bad it will not draw enough oil from the oil tank.
What we do in the shop is first verify that the pulser hose is good, after that we inspect the fuel line for vacuum leaks. If that looks good we pull the oil tank and dump it out, and see if there is trash in the bottom of the oil tank. And we also make sure that we can blow through the oil line. The pumps are fairly reliable, and 9 times out of 10 the problem is in 1 through 4. But if nothing stands out at the end of going through all of the hoes and the oil tank, then at that point we would replace the pump. Does that all make sense?