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Pull the aircleaner off when it won't run, and look down the carb throat while pushing back on the throttle. You should see fuel squirting down into the engine. If not, then you are running out of fuel.
A lot of the 460's had electric fuel pumps in the tanks with a fuel pump relay up front, and a oil pressure switch that controlled the relay. The relay was bypassed when starting, but power to the fuel pumps came from the relay and the oil pressure switch after the engine starts. People have a lot of problems with this system.