i looked at the diagrams for the 94/95 wrangler in FSM - look at pages 44 and 50 in the 95YJ_8W.pdf file. the coil side of the relay is the same (both positive and ground) for both ASD and FP relay. even more the feed for the contacts side is the same. so unless there is a wiring problem and assuming the connections are the same for your year you should have power at the asd when your FP relay gives power. i would check to see if there is a wiring prob there and if you have 12v on the coil and contact side of the ASD (again, assuming that your model is the same with 94/95).
from that document this is the description of how ASD operates
AUTOMATIC SHUT DOWN (ASD) RELAY
When the ignition switch is in either the START or
RUN position, it connects circuit A1 from fuse 4 in
the Power Distribution Center (PDC) to circuit A21.
Circuit A21 powers fuse 5 in the fuse block. Circuit
G50 from fuse 5 splices to power the coil side of the
Automatic Shut Down (ASD) relay. The Powertrain
Control Module (PCM) provides ground for the relay
on circuit K51. Circuit K51 connects to cavity 51 of
the PCM.
When the PCM grounds the ASD relay, contacts inside
the relay close and connect circuit A14 from fuse
1 in the PDC to circuit A142. Circuit A142 splices to
the generator field terminal, fuel injectors, ignition
coil, and heated oxygen sensor. Circuit A142 also connects
to cavity 57 of the PCM.
Circuit A14 from fuse 1 in the PDC supplies battery
voltage to the contact side of the ASD relay.
HELPFUL INFORMATION
˛ Along with supplying voltage to the ASD relay
contacts, circuit A14 supplies voltage to the contact
side of the fuel pump relay.
˛ Circuit G50 also supplies battery voltage to the
coil side of the fuel pump relay.
˛ Circuit A14 also connects to cavity 3 of the PCM.
J 8W-30 FUEL/IGNITIONYJ VEHICLES 8W - 30 - 1
BATTERY FEED
Circuit A14 from fuse 1 in the Power Distribution
Center (PDC) supplies battery voltage to cavity 3 of
the Powertrain Control Module (PCM).
HELPFUL INFORMATION
Circuit A14 also supplies power to the contact sides
of the Automatic Shut Down (ASD) relay and fuel
pump relay.