No horn operation for Pennsylvania state inspection

I have a 2004 Cadillac Deville. Just a beginner here. Has no horn operation when the air bag module is depressed. Horn works when relay is jumpered out or commanded with scan tool. I do not fully understand the wiring diagram, it has two fuses according too the wiring diagram both are good. One fuse under the steering colum looks like it would be on the ground side of the relay. Also has a dash intregration module. Any help would be appreciated.

You could be having issue with your horn plate or spiral, that connect the horn down side to th steering top. That flex can get damage

The dash integration module will activate the horn with the alarm, the key fob when you lock it, or the scan tool test.
The problem can lie with the fuse for the horn switch, the spiral cable(usually accompanied by an airbag lamp, but not always) or g200.
Unfortunately the wire color isn't clear from the diagram, but your could pop out the bag and check for 12v and ground at the horn switch.
You've pretty much proven the rest of the circuit is intact with the tests you've listed (good work BTW).