How do I repair horn in the steering column - 2004 Mitsubishi Outlander LS

If the horn sounds at all, to me, that means the horn relay is ok. The horn relay is in the underhood fuse box.
What you might try is a redundant ground wire from upper steering column support bracket to known good chassis ground.
I saw a service bulletin relating to horn ground on your vehicle, between steering column and chassis. if that is the problem, they have an improved steering column assembly, but, see if the jumper wire will work, first.

Clockspring in steering column may be bad .

The horn relay is NOT in the steering column. It's behind the left side of the instrument panel

The elements to a horn circuit in your vehicle are:

1. Steering wheel horn button;
2. Actuator wire in steering column;
3. Ground wire for steering column;
4. Horn relay; and
5. Horn.

Start troubleshooting!

the center section where the horn button is should slide out with some resistance. then one large nut holds the steering wheel on usually accompanied by 2 or 3 small bolts to hold the horn actuator down. it takes a gear puller to actually remove the steering wheel. as for the steering column itself it's a conglomeration of lag screws and plastic covers.

First of all, there is no wire that runs from the horn to the steering column (if the horn circuits had been properly diagnosed you would know this). I would recommend diagnosing and repairing the horn circuit the correct way rather than butchering your wiring harnesses and adding more problems to the electrical problems that you are already experiencing.

If you would like help with diagnosing and repairing your truck's horn circuit, I would be happy to help you do that.

You missed something putting the column back together. IDK the design of the wheel, but if all the wires to the column are good, I'd look at the switch itself in the column. Probably not making contact.

Sounds like horn contact under horn pad is grounding to steering column. Remove pad on steering wheel & try to repair connection.

The metal plate in reference above has small copper contacts. If they do not meet the horn will not work. We used a dremel on ALL of the contact point and it made no difference, the horn still only works about 5% of the time. After a whole lot of testing (I have the same issue with my 2000 Toyota Sienna) we found that the ground is weak, too weak for the relay most times. At this point I am going to run an alternate ground by "borrowing" the wire for the mute button for audio controls through the clock spring. The existing ground connects to the steering column. Before we discovered this I spent $285 on a new clock spring :(

A fuse always blows for a reason. The reason your fuse must have blown was because of a short to ground in the horn switch. That means the power side of the horn switch is currently touching ground or metal or that the switch is bad on the inside. The more remote possiblity is that you have a short somewhere in the wiring harness. It is always typical for a component to go bad before a harness.

Here are some notes directly from chrysler, let me know if you need any clarification:

Testing and Inspection Notes WARNING: ON VEHICLES EQUIPPED WITH AIR-BAGS, REFER TO AIRBAGS AND SEAT BELTS/AIRBAGS BEFORE ATTEMPTING STEERING WHEEL, STEERING COLUMN, OR INSTRUMENT PANEL COMPONENT DIAGNOSIS OR SERVICE. FAILURE TO TAKE THE PROPER PRECAUTIONS COULD RESULT IN ACCIDENTAL AIRBAG DEPLOYMENT AND POSSIBLE PERSONAL INJURY.

1. Disconnect and isolate the battery negative cable. Remove the lower steering column cover/knee blocker. Check for continuity between the metal steering column jacket and a good ground. There should be continuity If OK, go to Step 2. If not OK, refer to Steering and Suspension/Steering Column and check for proper installation of the steering column mounting nuts.
2. Remove the driver's airbag module. Unplug the horn switch wire connector. Remove the horn relay from the Power Distribution Center (PDC) . Check for continuity between the steering column half of the horn switch feed wire connector and a good ground. There should be no continuity If OK, go to Step 3. If not OK, repair the short circuit as required.
3. Check for continuity between the steering column half of the horn switch feed wire connector and the horn relay control circuit cavity for the horn relay in the PDC. There should be continuity If OK, go to Step 4. If not OK, repair the open circuit as required.
4. Check for continuity between the horn switch feed wire and the horn switch ground wire on the airbag module. There should be no continuity If OK, go to Step 5. If not OK, replace the faulty horn switch.
5. Depress the center of the airbag module cover and check for continuity between the horn switch feed wire and the horn switch ground wire on the airbag module. There should be continuity If not OK, replace the faulty horn switch.