It seems that the wire is so short that I cannot insert it into the back of the horn button let alone tighten the tiny little set screw. There doesn't seem to be any slack in the wire to pull it out of the column further. Is there a trick that I am missing here? Thanks!

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I would solder an extension of wire to the short piece inside the hub and then you will have enough to make the insertion into the button. Of course, after soldering the new wire, wrap with plastic or electrical tape to prevent the horn sounding off at inappropriate times.

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Adding some wire was my plan B. I only need to extend it enough to get at the set screw. An inch should be more than enough.

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