Does it have the electric solenoid in the base of the carburetor? With engine cold, flip key on and off, listening for the click of the solenoid. Learn the sound, Then when engine quits, flip key on and off, listening for the click. No click, no fuel. This solenoid closes the main jet in the carburetor when it closes. Has to have 12 volts to it at all times the key is on. It may be getting hot and closing the main jet.
with twin engine, I always want to check t be sure both cylinders are firing! If you can, loosen the spark plug wires and with engine idling, remove one wire at a time, engine should continue to run, if engine dies when wire is removed, the opposite cylinder is not firing. Check it for spark and compression, and if it has both, check the pushrods.
If it has spark and both cylinders are firing, do you have fuel getting to the carburetor from the fuel tank? Is this a gravity flow to carburetor, or does it have the pulse fuel pump?
Yes, pulse pump, and the hose from rocker cover should have a slight pulse when cranking.
Good job! Thanks!