My T-Bird started to stall when starting from stopped so I changed the fuel filter and that seemed to fix it. Now with cooler weather it has stalled several times from stopped position and it will only start again with continued pumping of the gas peddle. Does that sound like a bad fuel pump or something else? It has a 5 Litre fuel injected engine with 130,000 miles.
It's possible that you fuel pump is failing but it is also possible that your TFI Module is failing too. You need to first determine if your car is losing fire or fuel. You should never have to pump the pedal of a fuel injected vehicle. If it were up to me: Hook up a scan tool and retrieve any codes from the computer (EEC-IV) system. A MAP sensor failure can cause a stalling problem - so can a carbon-laden EGR valve. Hook up a fuel pressure gauge and test the fuel pressure and volume (yes, I've even secured the gauge to the windscreen to watch the pump while I drive it) and have a spark tester handy for when it does stall to check for a lack of spark.