I had this recently on Big Blue. Turned out the horn was bad. The relay is what is clicking, and it then sends power to the horn.
I tested the horn by placing jumper wires on it and hooking it directly to the battery. In my case it did nothing. So I grabbed another and got a timid beep. Sprayed contact cleaner into the horn, held upside down so it would run in, and finally got it working sorta.
I turned to the other one, but the contact cleaner didn't help. Then I accidentally dropped it and it started working.
Gary, AKA "Gary fellow":
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Dad's: '81 F150 Ranger XLT 4x4: Down for restomod: Full-roller "stroked 351M" w/Trick Flow heads & intake, EEC-V SEFI/E4OD/3.50 gears w/Kevlar clutches
Blue: 2015 F150 Platinum 4x4 SuperCrew wearing Blue Jeans & sporting a 3.5L EB & Max Tow
Big Blue: 1985 F250HD 4x4: 460/ZF5/3.55's, D60 w/Ox locker & 10.25 Sterling/Trutrac, Blue Top & Borgeson, & EEC-V MAF/SEFI