Hi Frank
Good thinking on your part to do the FOB test says a lot about horns themselves, relays, ground etc
How horns work :
Battery voltage is supplied to the coil, and switch of the horn relay #36, in the underhood electrical center. The horn relay coil is energized when circuit 28 is grounded.
This may be done through the horn switch on the steering wheel, or through the Body Control Module when the horns are used as an alarm or a signal, for the Universal Theft-Deterrent System.
When the horn relay coil is energized, the normally open horn relay switch is drawn closed, and battery voltage is supplied to the horn feed circuit 29 through the horn fuse #11.
Common fault is the horn brush in steering wheel

Easy test with as below is that horn relay, push horn area of top of steering wheel and see
if ground than shows up as I pointed to
If no ground, then have to take airbag off to see horn switch or horn brush
Or maybe that wire from that to the relay
