[2.7RACER]

Pete and Brian,
Brian's analysis is good except the air flow switch opens once the air flow sensor rises with the engine running.
Once the engine is running and the air flow sensor held up, the air flow switch is OPEN, this breaks the control power to the fuel pump relay.
With the fuel pump relay not energized, power flows to the fuel pump from the fuel pump fuse.

In essence when the engine is running the fuel pump relay is NOT energized. Not what you would at first expect.

Thus the wires which connect to the air flow switch should NOT be connected together for the fuel pump to run.

Connecting the air flow switch wires together will energize the fuel pump relay, which blocks power to the fuel pump, except during the cranking process.

The problem here is the circuit is designed as Brian pointed out to control fuel flow only when starting or running.
Bypassing the air flow switch allows the fuel pump to run as soon as the ignition is turned on.
If the engine is not cranked right away the injectors will flood the engine with fuel.
Likewise if the engine stalls while the ignition is on, the fuel pump will continue to run flooding the egine with fuel.

So Pete, your engine will start and run with the wires disconnected, but it can flood easily if not cranked right away.

Or if it stalls and the ignition switch is not turned off quickly it will flood.