Looks like you have a repro horn button assembly. Its junk. Try to get a GM one or maybe CHQ makes one. I had the same issue years ago.
The white snaps that hold it all together are protruding into the area in which the button ring goes into. If you're dead set in using this one, try spinning the white snaps around so that the button itself can go deeper into it. Looks like the bottom one is broken off because of that reason.
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