I'm documenting this for posterity, so others can learn from my troubles.

My CJ headlight switch went bad, and the replacement switch would not grab
the shaft of the ****. I went and got another switch, verified in the store
that it would grab the shaft, installed it, and it wouldn't grab the shaft.
Took it back, and the others in the store wouldn't grab either. It turns
out, the switches are now made in Taiwan, and they made with slightly
different tolerances than the original. It appears that I might have even
damaged the one switch by verifying it would grab the shaft. The solution
is to purchase a replacement shaft (NAPA part# 735-2789) which is tapered
differently on the end, and will work with the new switches.