Below is from a 96 FSM, but I suspect your 98 is the same in this area. If you don't have one already I suggest Google to find a Factory Service Manual for your 98. Chances are you can find a pdf download. But in case you can't / don't find 98 see below. If this doesn't help I will lookup how to post pictures and grab the schematics. Just haven't tried to post any since the change. What I see in them though is power comes from the start / run side of the ignition to both the ASD and FP relays through fuse #9 (10A). The ground side comes from the PCM on both to control switching. Can't say I understand your statement about the voltage floating. But to answer your question, there are several inputs to the PCM that can kill the switching of the relays. If you have a fuel pressure test gauge, connect it and crank the engine to see if you are getting any pressure even momentary. If so, it could be your crankshaft position sensor.

FUEL PUMP RELAY-PCM OUTPUT
The PCM energizes the electric fuel pump and the
oxygen sensor (02S) heating element through the
fuel pump relay. Battery voltage is applied to the fuel
pump relay when the ignition key is ON. The relay is
energized when a ground signal is provided by the
PCM.
Refer to Automatic Shutdown Relay—PCM Output
for additional information.
The fuel pump will operate for approximately one
second unless the engine is operating or the starter
motor is engaged.
The fuel pump relay is located in the Power Distribution
Center (PDC) (Fig. 19).

AUTOMATIC SHUTDOWN (ASD) RELAY—PCM
INPUT
A 12 volt signal at this input indicates to the PCM
that the ASD has been activated. The ASD relay is
located in the Power Distribution Center (PDC) (Fig.
2). Refer to label on PDC cover for relay location. The
relay is used to connect the oxygen sensor heater element,
ignition coil, generator field winding and fuel
injectors to 12 volt + power supply.
This input is used only to sense that the ASD relay
is energized. I f the powertrain control module (PCM)
does not see 12 volts at this input when the ASD should be activated, it will set a diagnostic trouble
code (DTC).

Do you know if any codes are set? Key on/off sequence to get codes.

Also from the FSM:
GENERAL INFORMATION (Continued)
The PCM monitors the crankshaft position sensor.
If the PCM does not receive a crankshaft position
sensor signal within 8 seconds of cranking the
engine, It will shut down the fuel injection system.
The fuel pump is activated by the PCM through
the fuel pump relay.

So if your just turning the key on, or cranking for a few seconds and then checking for voltage, the PCM may have well already opened the ground circuit.

Testing the relays;
ASD AND FUEL PUiP RELAYS
The following operations/tests apply to these
relays only: Automatic Shutdown (ASD) and Fuel
Pump. These relays are located in the Power Distribution
Center (PDC) (Fig. 55). Refer to label on PDC cover
for relay location.
The relay terminal numbers from (Fig. 56) can be
found on the bottom of the relay.
Fig. 55 Power Distribution Center
• Terminal number 30 is connected to battery voltage
and can be switched or B+ (hot) at all times.
• The center terminal number 87A is connected (a
circuit is formed) to terminal 30 in the de-energized
(normally OFF) position.
• Terminal number 87 is connected (a circuit is
formed) to terminal 30 in the energized (ON) position.
Terminal number 87 then supplies battery voltage
to the component being operated.
• Terminal number 86 is connected to a switched
(+) power source.
• Terminal number 85 is grounded by the powertrain
control module (PCM).

TESTING
(1) Remove relay before testing.
(2) Using an ohmmeter, perform a resistance test
between terminals 85 and 86. Resistance value
(ohms) should be 75 ±5 ohms for resistor equipped
relays.
(3) Connect the ohmmeter between terminals number
87A and 30. Continuity should be present at this
time.
(4) Connect the ohmmeter between terminals number
87 and 30. Continuity should not be present at
this time.
(5) Use a set of jumper wires (16 gauge or smaller).
Connect one jumper wire between terminal number
85 (on the relay) to the ground side (-) of a 12
Volt power source.
(6) Attach the other jumper wire to the positive
side (+) of a 12V power source. Do not connect this
jumper wire to relay at this time.
CAUTION: Do not allow the ohmmeter to contact
terminals 85 or 86 during these tests. Damage to
ohmmeter may result.
(7) Attach the other jumper wire (12V +) to terminal
number 86. This will activate the relay. Continuity
should now be present between terminals number
87 and 30. Continuity should not be present between
terminals number 87A and 30.
(8) Disconnect jumper wires from relay and 12 Volt
power source.
(9) I f continuity or resistance tests did not pass,
replace relay. I f tests passed, refer to Group 8W, Wiring
Diagrams for (fuel system) relay wiring schematics
and for additional circuit information.