<p>Hi from JustAnswer! This answer asumes a factory 5.0 carbureted Mustang.</p><p> </p><p>All vintage engines use a mechanical fuel pump, and yours is mounted on the engine block. You are probably running out of fuel either because the pump is worn or there might be an air leak into the hose supplying the pump from the tank.</p><p>First, check for and repair any visible gasoline leaks between the tank and the fuel pump. Then, do a fuel volume test by cranking the ngine for several seconds with the fuel line disconnected from the carburetor bowl. You should see at least 10 oz of gasoline after cranking for 15 seconds. If all this works, you should be able to supply the carb adequately for starting and idling.</p><p> </p><p>If fuel volume is just fine and you still have fuel starvation after running less than a minute after startup, replace the fuel filter located on the carburetor fitting to the fuel line. Never operate a carb without a filter. </p><p> </p><p>The carb has an internal valve that allows only a certain amount of fuel into it at a time. This needle-and-seat valve can stick closed and cause no-start, but seldom lets the engine run for any length of time. For you, chances are better that the fuel supply is falling off, or another possibility is that it's choking due to a bad adjustment of the choke thermostat. Most times, though, this results in a flooded engine that won't start at all.</p><p> </p><p>Considering the mileage of the engine, the cam lobe which drives your mechanical fuel pump may have worn down. If this is the case, even a new mechanical pump won't function properly and the only practical repair is to upgrade to a low-pressure electric fuel pump which you can mount on the frame inline, instead of through the old pump. Maximum pressure for carbureted cars should be about 8psi, no higher or you will overpower the needle-and-seat valve.</p><p> </p><p>Luckily, there are no complex electronic controls on the ignition side of your car. At worst, a possible ignition cause might be a broken ignition pickup coil, which has wiring that can bend off and break inside the distributor - this causes very erratic operation under different conditions but also accompanies a violent tachometer signal and some brutal driveability misfire - which is a telltale of an ignition problem instead of a fuel problem.</p>