Matt - I don't remember seeing any specs for the horns, just "high" and "low". And I don't have spares since many of those on the trucks I've owned have been bad.
But I have been able to get some of them working. The thing that typically goes wrong is that the electrical contacts don't make a circuit, and I've sprayed contact cleaner in them and gotten them to work. But sometimes even that doesn't work. On one I dropped it, quite by accident, and it started working. Apparently that caused the contacts to make a circuit.
However, if I remember correctly the horns have an adjusting screw which changes the frequency. Does the new one you picked up have that? Can you "tune" it?
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