So good news...I got my horn working. I cleaned the contacts under the air bag, which were very dirty, and the horn worked a bit better but not as consistently as I would have liked. But, whenever I pressed it I could hear a click coming from the horn, yet the horn wasn't sounding. It was enough to establish that the switch was working, however. Clearly, there was too much resistance somewhere in the circuit...so I checked the fuse. It was rather oxidized, so I cleaned up the contacts on it and the holder. Now the horn blows very consistently!

Thanks everyone for all the help and useful information!