It says that in earlier model FSMs like for my 97, as quoted below.I don't see where it says that anywhere.
But it appears we are both right depending on the model year. My '97 TJ's ASD relay directly controls the fuel pump relay, I knew that's how my '97 worked when I entered into this conversation.
'97 FSM page 14-26
AUTO SHUTDOWN (ASD) RELAY-PCM OUTPUT
The ASD relay is located in the Power Distribution
Center (PDC) (Fig. 2).
The ASD relay supplies battery voltage to the fuel
pump, fuel injector, ignition coil and both oxygen
(02S) sensor heating elements. The ground circuit for
the coil in the ASD relay is controlled by the Powertrain
Control Module (PCM). The PCM operates the
ASD relay by switching the ground circuit on and off.
How the above works changed in later years. The below is out of the 2005 FSM...
OPERATION
The Powertrain Control Module (PCM) energizes
the electric fuel pump through the fuel pump relay.
The fuel pump relay is energized by first applying
battery voltage to it when the ignition key is turned
ON, and then applying a ground signal to the relay
from the PCM.
Whenever the ignition key is turned ON, the electric
fuel pump will operate. But, the PCM will shutdown
the ground circuit to the fuel pump relay in
approximately 1–3 seconds unless the engine is operating
or the starter motor is engaged.
The later years including the 2005 uses the ASD relay as one means to tell the PCM when the engine has stopped running. When that happens the PCM will then remove the enabling ground signal to the fuel pump relay shutting it off.