Do you have an air bag light lit on the instrument cluster ? Do you have C.C. button's on the steering wheel , do they work ? If the alarm fob (as u call it ) Can make the horns sound , the relay is sending B+ voltage to the horns Don't know how your testing.
System Description
The horn system consists of the following components:
• Horn fuse
• Horn relay
• Horn switch
• Horn(s)
• Body Control Module (BCM)
System Operation
The vehicle horns are activated under the following conditions:
• The horn switch is depressed.
• The body control module (BCM) commands the horns on. The BCM commands the horns on under either of the following conditions:
- When the content theft deterrent system detects a vehicle intrusion. For further information, refer to Content Theft Deterrent (CTD) Description and Operation in Theft Deterrent.
- When the panic button is depressed on the remote control door lock transmitter. For further information, refer to Keyless Entry System Description and Operation in Keyless Entry.
- When the OnStar® system is used to sound the horns, if equipped. For further information, refer to OnStar Description and Operation in Cellular Communications.
- When the keyless entry system is used to lock the vehicle, a horn chirp may sound to notify the driver that the vehicle has been locked. The notification feature may be enabled or disabled through personalization. For further information, refer to Keyless Entry System Description and Operation in Keyless Entry.

Circuit Operation
Battery positive voltage is applied at all times to the horn relay coil and the horn relay switch. Pressing the horn switch applies ground to the horn relay control circuit. The body control module BCM may also apply ground to the horn relay control circuit as described above. When the horn relay control circuit is grounded, the horn relay is energized and battery positive voltage is applied to the horn(s) through the horn control circuit. The horn(s) sound as long as ground is applied to the horn relay control circuit.