There are two horns actually and they are located between the low between the grill and the radiator and are hard to get to or see because of the radiator shrouding and the strut work that supports the front fascia of the grill.
Right behind the grill
Its located behind the front bumber on the drivers side. Under the turn signal lamp.
under the passenger side of the front bumper, this can be veiwed from below
I have a jeep Cherokee of that year and I believe that what you are refering to is a spherical thermometer and horn assembly.
The controls are on the steering wheel. Inside, the horn is mounted in the front driver side fender area kind of behind the front bumper.
You have to look up under the passenger side front bumper. on the steering wheel. there are two buttons with pictures of horns on them.
Very carefully
The horn on the 1997 Jeep is located on the steering wheel. The actual sound part (horn) is located under the front right side of the front bumper. If you stand in front of the jeep and stick your hand in the left most cutout hole on the bottom of the plastic bumper cover, you can touch the dual horns as well as remove them and replace them.
Left front inner fender next to the air cleaner box
If the fuses are good on a 1996 Jeep Cherokee and the horn still will not work, check the horn relay switch on the passenger side fender wall inside the engine compartment. Also check to make sure that the horn is hooked up properly.
i have a 1992 Cherokee limited on it its under the lower pannel to the right of the streeing wheel
Under the hood there is a 5 in. Long bl. Box to the left facing the jeep. There are fuses in it, the horn fuse is in there....good luck..