1998 Jeep Cherokee replaced headlight switch, now they don't work

Best guess is the Hd. Lt. Relay.
Probably will have to be replaced.

It can be issue with headlight switch,but as its already been replaced.Try disconnecting high beam headlight wiring from headlight assembly and reconnect direct external wire from headlight switch to headlight assembly,then by switch see if headlight is getting off and turning on or not.
See below related help links,similar to your issue.Click the link below:----
Only high beams work but head lights not working on Ford F350?

http://howtobyme.blogspot.com/2011/11/only-high-beams-work-but-head-lights.html

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---------- • Working of Headlight switch? ----------

• Both headlight bulbs blow together? ----------

• Car headlight bulbs don't last long?
------------ Only one head light works on 2001 Dodge Caravan? http://howtobyme.blogspot.com/2011/11/only-one-head-light-works-on-2001-dodge.html

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these will help.
Thanks.

You have separate fuses for high/low beams. Check that.

I'm going to post this in the clarification section. I don't have a wiring diagram for a 96 Grand Cherokee headlight circuit.
The 95 models used a circuit breaker built-into the headlight switch. The 97 models used a fuse in the fuse box. If your model uses the headlight circuit breaker, a short in one of the headlights or the wiring harness would trip the circuit breaker in the switch. You could unplug one headlight at a time to see if it continues to go on and off.

CHECK HEADLIGHT FUSE OR CIRCUIT BREAKER IF ALL IS GOOD.YOU COULD HAVE FAULTY HEADLIGHT SWITCH OR FAULTY DIMMER SWITCH.

If your headlight switch is the type you pull out, left of the sterr column on dash, switches tend to go bad, I replaced mine and only had 50,000 miles. try checking headlight relay in engine fuse box first.
.

if you checked the fuses for the headlights,pull back on turnsignal handle to see if you have high beam over ride,
if you do i would think it was the headlight switch

I would look at replacing the headlight switch(junkyard will save you money)!

Hope this sheds some light on it!

Soounds like you have a wire problem. Look under your dash at the headlight switch and the connector for any melting....repair as necessary. Look also around the headlight wiring....sounds like you have a wire that is shorting out.

had the same problem on my 92....check under the hood on the drivers side,towards the front,there is a "junction box" with all of the lighting wires connecting from the switches to the lights.My wires were all corroded inside,so I cleaned the ends and bought a new box from the local electronic supply store.The problem has not come back.

Cheers