Okay, backup lights, signals, and taillights  are good but the "running
lights" that come on with the headlights are not?

First of course, check the bulbs.  It COULD be both bulbs.  Make sure the
headlights work.

On some cars the headlight relay turns the things on, and a bad headlight
relay can cause an issue like this.  But that's the point at which you
need to get out a meter or a test light... make sure there is no voltage
at the socket and no voltage at the headlight relay output before you
swap the relay out.

And of course there are lots of connectors in there, and that car is old
enough that connectors may be starting to fail.  

Having a shop manual makes this sort of thing a thousand times easier
because it tells you how everything is wired and where all the connecting
points are.
--scott

If the fuse under the dash is bad, the dash panel lights will be out as
well as the front running lights.  The fuse for the tail lights is the
at the top right of the panel under the dash by the driver's left foot.

If the fuse is ok, then I would suspect the bulbs next, then the ground
tag, then the trailer hitch wiring connection which is usually under the
kick panel under the spare tire if factory.

Mike
86/00 CJ7 Laredo, 33x9.5 BFG Muds, 'glass nose to tail in '00
88 Cherokee 235 BFG AT's
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back lights wont go on 1988 jep cherokee , fuse box? ..... "THINKIN"

Depends on which back lights.   The back of a jep
could have tail lights, parking lights, marker lights,
stop lights, turn signal lights, backup lights, etc.
Please; more info about the problem with your jep. ............Rodan

lol    Brake lights work but tail lights don't. I replaced
all the fuses still nothing.    Is there another fuse box
besides under neath the steering wheel?   ................... "THINKIN"

The front marker lights and the tail lights are on the same
fuse, so if the front marker lights operate the fuse is okay.
Then the most likely cause is a bad ground at the tail light.
Be sure the ground wires from both tail light sockets are
firmly attached to a clean metal grounding point.   A less
likely cause is a broken power wire to the tail light sockets.
Turn on the tail light switch and check for 12 volts at the
ends of the wires where they meet the sockets.   If there
is no voltage, trace the wire back to the switch to find
the break.                                     Good luck. ................Rodan.