73T with CIS? If so, it could be the fuel accumulator. When the fuel accumulator was faulty on my old 2.7, I could get the engine to start quickly by lifting the sensor beam and letting the fuel pump run for a few seconds just like you mention. The fuel accumulator's primary purpose is to damp out pressure pulses in the fuel system, but it also acts to maintain fuel pressure for starting. If the diaphragm leaks, you lose the maintenance of fuel pressure and hence letting the fuel pump run for a few seconds rebuilds this pressure and it starts.
If you car is MFI, I don't have a clue.
