...and a lot of cars pump for 5 seconds when you turn the ignition on but then stop until the car is cranked.
You are not chasing a non-existent fuel pump problem are you?
You did say that the pump ran when you put 12v on it so the pump works.
I quote....
In contrast to more modern engine management systems, the 14CUX controls fuel delivery only; it does not control spark ignition. On 14CUX-equipped vehicles, the spark control is done mechanically with the use of a distributor.
When the ignition is first turned on, the ECU energizes a relay that runs the fuel pump for a short time to pressurize the fuel rail. Once the starter motor begins to turn the engine, the ECU gets a 12VDC signal that causes it to run the fuel pump again, and energize the fuel injectors. For the next several seconds, the injector pulse width is wider than normal to provide sufficient fuel for starting. Idle control is performed by adjusting a stepper-motor-driven bypass valve in the intake plenum. When the ignition is switched off, the ECU winds the bypass valve fully open to provide enough air the next time the engine is started.
To determine the amount of fuel required by the engine, the ECU reads a number of sensors measuring the following factors:
Intake air mass
Coolant temperature
Engine speed
Throttle position
Fuel temperature
Exhaust oxygen content (narrowband)
Road speed
The intake air mass is measured with a "hot-wire" mass airflow sensor: drawn in by intake manifold vacuum, air moves past an electrically-heated wire filament, and the degree to which the filament is cooled indicates the mass of the airstream.
