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Do you have a good ground at the horns, try connecting a good ground to the black wire on the relay, does the relay operate? If no, check the fuse, on the 84 its the ctsy/clock fuse, on the 86 its the theft fuse.. The 85 s/b one or the other..
From: 1994 LT1 Coupe 6-speed with FX3 & 2000 LS1 Vert 6-Speed with F45 Hunterdon County, NJ
Do the horns work normally (i.e. when you press the steering wheel center edge?
If so, then check the owners manual to assure the alarm is enabled.
Also, check the door switches as if stuck or failed elecrically they will not tell the CCM when the door is open/closed and thereby prevent the alarm from activating.