After reassembling one of our fans for the summer yesterday, I noticed that it was no longer oscillating. Normally I would have left it and shaken my head at the poor engineering every time I used it in the future but yesterday I ended up with an unexpectedly free afternoon and decide to have a look. My solution, comprised of a paper clip and probably a yard of electrical tape, is pictured above. And guess what? The fan now oscillates.
In memory of my father-in-law, an artist of the improvised solution and "special method," on Father's Day.