Interesting problem. That retainer ring is actually a spring-loaded electrical switch that makes a connection between the horn relay wire that comes up the column, and ground at the steering post. I would pull that "retainer" again and look it over carefully while squeezing it together, make sure nothing is warped, and also maybe run some fine emory cloth or sandpaper in between the "wafers" (the two flat surfaces) then blow it clean with compressed air. Then orient the retainer so that the logo lines up and tighten it down, stick the horn button on and give it a try. Sometimes (often?) new electrical parts need a little fenagellin'. Also check the surface of the steering wheel that contacts the retainer, make sure it's not dinged or burred.
Dang, this oughta work, I like that bowtie logo. It'd be a shame not to be able to use it.
