Lets clear up some incorrect assumptions and information.
There are 3 horns on the truck. The S-horn is located on the right fender behind the air filter box. It is associated with the security system, has it's own "s-horn" relay, and is powered through the security fuse. The road horns (2) are behind the front grill, are powered through the "horn" fuse and the "horn" relay. Two different circuits.
The sounding of the security horn on lock/unlock (if enabled)
or panic button on the fob is NOT an indication of the condition of the "horn" circuit. That event is all on the "s-horn" circuit.
The road horns fuse and relay are located on/in the "integrated relay" also referred to as 'Unit K' in the manuals. This module is in a slot at the rear of the fuse/relay box.
Top view:
Inner map:
Looks like this:
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Since smoisan says that the relay can be heard clicking when the steering pad is pressed then the button, spiral coil, and all ecu connections up to the relay are good and the circuit is complete up to the integrated relay.
I would start at the horns with really basic checks. Does the wire connected at the horn look good as far back as you can visually trace it? Is there +12v at the connection with the horn when the steering wheel pad is pressed? If the wires look good and there is no power then it's either hidden wire damage or the integrated relay is suspect.
The integrated relay can be bench tested and tested in place. I can give you the procedure for that if needed. But first do the really basic checks.
Might be as simple as a critter damaged wire behind the grill.