Sometimes (when there's nobody else near me), I try different movements with the steering wheel to try to get the horn to sound. But nothing so far, it appears the gremlins are

when I want it to happen. I hadn't thought about the relay...maybe replacing that would work.
As far as the keyless entry, I'll have to check that. I have my memory settings saved so that the lights flash when I arm/disarm, but without sounding the horn. I'll have to change that setting and see if it is the same duration as when the gremlins play...

Thanks for the input. I hadn't thought about the alarm, either.