What size is that bolt?

As mentioned previously, I discovered the horn of my motorcycle dangling, held only by the wires meant to activate it. There's a single bolt on the back that sticks in an accessible hole on the chassis, onto which a nut is supposed to hold it.

The bolt measures 9/32" by the drill sizing tool I have. I tried 1/4" (a touch too small) and 5/16" (way too big) with no luck. I picked up an assortment of 6-8mm wingnuts at an auto-parts store, and found one that fit, but didn't quite hit the threads right.

It's holding, but what kind of twisted piece of metal will I end up with before I find the correct nut? I'm looking at new horns now, and they're only $10-ish. Seems a lot more expensive than a new nut, until you figure the hour I've invested in tinkering on my knees bending under the bike, and the $4 the assortment of wingnuts cost me.