Horn spontaneously go off and will not stop unless the fuse out

Check your fuses. It varies from car to car but you may have a fuse dedicated only to the horn unit. In that case you can just pull the fuse without affecting anything else..

Other than that you will need to pull the wiring connectors off the horn unit and tape them up to keep any moisture and dirt out. Hopefully that will not trigger any issue with the security system.

gotta love bad advice,
KJ car
and you failed to scan the PCM, so you really dont know
what system in the car set off that alarm of the 3 or 4 possible.
so, ill not guess.
to fix cars or advise, one must know how this car works.
and Tralaina dont.
the 05 KJ , FSM book is free to view. linked below'

the first answer is pull the horn RELAY,
do not pull FUSE JB F11, this kills other vital systems.
unplug horn actual or the relay (for a nice stop gap fix)
long gap, (LOL)? fix sure.
scan the PCM and win.

the horn switch activates the horn relay
as does the BCM.
but wait what causes BCM to honk horn.,
lots of things.
alarm, inputs WRONG
key fob door lock access. controls , gone wild.
and more, i dont have all programming of BCM, facts.
but is not important , what does matter is SCANNING the PCM.

YOU will get DTC errors, and now you know, WHY and WHAT
set off the alarm.

the JB is drivers cab box. J11 will kill
Pulled
sun roof
and power windows. (my guess is that is important to you)
if you pull that top fuse in PDC box, lots more dies. lots.

There is a "clockspring" wiring spiral in the steering wheel to accommodate the rotating steering wheel with controls on it. If this breaks, you may lose some or all functions controlled by stuff on the s-wheel.

The contact points in the horn button get dirty or stuck sometimes may cause that or check the horns connections under the hood:)

You will need to replace that "stop horn" fuse since it also feeds power to the stop lamps and the gear shifter solenoid, when you step on the brake pedal. Your best bet is to unplug the horn on the vehicle(to stop it from honking) until you can get it fixed. That way, you will be able to shift out of park to get it to a shop for repairs.

It is likely the button in the steering wheel has shorted out. Unless you can get it to stop by pulling up the button, the steering wheel will have to come off for repair; and this requires special tools. In the meantime, you can pull the horn relay out of the fuse box and reconnect the battery.

Check the horn relay - it might be stuck. If the horn is OK then the only thing left is the horn button - pull out its wires, if the horn stops then the button is broken if not then its the relay.

If you can locate and pull relay, do that, if not, pull wires off at horn if you can, otherwise pull fuse. If you have other relays same in area of horn relay (same number on relay) try one of them in that horn spot to see if maybe it's just a stuck relay.If you pull fuse for horn, you may find out something else on same fuse, so make sure you check everything else is working.

Check the fuse and relay centre under the hood. Look for a relay marked "Horn". (The map should be on the fuse box lid.) Pull it out and exchange it with the A/C fuse ONLY if it is the same part number. Replace your fuse and try it. If this does'nt solve it you can get the car in gear by using the manual gear release located by the shifter nob. Just insert a spare key and pull selecter back. The automatic release solinoid must be on the same circuit as the horn.

I have the same problem.  I pulled the fuse out, in the box under the hood, on the passenger side of the engine, by the coolant overflow.  It killed my horn issue.
Funny enough, the only part of my horn that I miss is the beep when locking my car.  I don't really use the horn and perhaps when some idiot cuts me off one day, I'll be sorry.
I just had my AC Rad fail, and fixed that today.  I am picking up my Jeep tomorrow, and have asked the mechanic if he has any ideas.