2004 WJ and as always wires and connections can fail.
the chapter on rear lighting covers this in 8w
page 8w-51-7
shows the backup relay.
see that?
jb fuse F20, Jb is cab fuse. 10amps.
that be first, measure it with an Ohmeter (DMM set to resistance RX1) 0 ohms is good, more bad.
on this car the shifter controls the relay, not the BCM or TCM or PCM.
the shifter, does
page 8w-31-15
seen below, the red arrow drives said relay
the book is free on line, posted by me 300 times, WJ jeep
or go to mitchells and read, at any time.... you want.
the assy below runs off 2 other fuses.
JB f12 and f21
did you scan the PCM first. to see if there are error from the below.
The below uses the PCI bus network , so.... we scan it first.
eg; lost comm's to shifter assy. DTC error.
it be wise to check all fuses first.
or scan it first.
i cant see what your SA is doing so... can not wax too smart.
this is SA.
fixing complex cars like this, the service manual is manditory
as is a scan tool.
other wise, just wild guessing , happens.