So the solution proposed above worked perfectly - undo the RS3000 G-R wire under the steering column that is tapped into the factory G-R horn switch wire. No more horn sounding if/when the alarm goes off!
Here is where the G-R wire taps into the horn switch G-R wire:
Here are the wires with the tap removed:
And the stripped portions covered with electrical tape:
Of course I just had to try it out, so I locked myself in the truck, then opened the door manually. Sure enough, the alarm went off, lights flashing, and the little piezo chirping quietly, but no horn! Perfect!
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1997 4Runner Limited 4WD E-Locker ~200k | Falken Wildpeak A/T3W 265/75/16 | Pro Comp 69 16x8 | OME 2906 | B&M 70264
Addicted Offroad Front Bumper | Spiker Engineering High-Lift Hood Struts and Ultragauge Mount