97 TJ reverse issue

i think you ment IP cluster backlights dead not warning ligts
that is real the huge parking light structures.
a blown fuse. it is, why not test them ? first.

either cab fuse or the engine bay fuse box.
12vdc on both sides of fuse, is a good fuse, key on.
100% accurate test. no guessing. ever with voltmeter.
(rare exceptions a car with a ground fuse, very rare)
so lets do this the hard way, no fuse tests......

but hark the fsm is free. why not just look at the road map er, schematic, (wiring diagrams)
lets do HL , they are hot all the time, keys lost .

your car is a TJ so having a TJ book is spiffy , no? KEEN?
lets do that. TJ wiring
click TJ
http://www.jeep4x4center.com/knowledge-base/index.htm?utm_source=cj#service

now click wiring, following me?
posted this 100 times,., here.

my guess is parks are dead High beams good, right, ?????
yes then go to JUMP 1.
HL dead highs and low beam? parks out.(aka TAIL)
PDF page # 92
fuse PDC #17 blown? kills cluster dead too
JUMP1: parks dead.
had lamps is fuse #1, jb (page 134 pdf)
then PDC fuse 4 and 10 (lows and highs)

PDC is engine bay box.
JB is cab box.

so my guess (hard way)
fuse 10 and CB 24 was blown. kills high/low beams
Fues1 and 4 only parks. and cluster dimmer feed.

page 134 makes all this childs play with a meter.
volt meter.

Is the ground cable from body to engine OK/secure? Any other electrical anomalies?

I had the same problem with my 97 Tj and all you have to do is purge the water system it has air in it

ignition control module needs to be tested, it controles the coil.

There is no shut off. You have to pull the fuse behind the glove box! I know I got one.

Had similar problem on 98 Jeep TJ, sometimes go sometimes turn over but would not start, turned out to be a corroded wire the the pcm deep down beside the battery, once wire was repaired it was fixed. The week wire gave some volatage but not enough to start it every time. Good luck!

is the check engine light on?

I have a 97 TJ and the headlights wouldn't come on but the parking lights would. Funny thing was that if I pulled the brights to flash someone, the brights would work. I took out the old headlight switch ($26 at Checker) and they work again. When I pulled the switch there was one connector that seemed to be corroded. Hope this helps

Why it is random I can't guess, but what you describe sounds like ignition timing change perhaps from a worn distributor. If you own or can borrow a timing light to see if the timing is jumping around, pulling the distributor can be avoided if the timing checks out as steady.   

If you pull it, mark EVERYTHING first(!) and inspect the drive end of it and its seat to see if there is any excessive wear to be seen.

Make sure you have the right bulbs in the back. it sounds like a cross feed.If the problem isn't there then i'd say the turn signal switch is bad.