This item has always intrigued me. I believe I have an idea what it might be - the governor from a music box.
I am going by memory of what the item looks like as I can't find the particular TIGHAR Tracks that had a sketch.
If this is correct then the two holes on the 'wings' would have secured small pieces of flat steel by means of small tubular rivets. The length/area of these flat pieces would have been ground in length/size to set the tempo of the music. At one end would have been gear teeth to connect it to a larger gear on the. If these teeth are oriented in the axial direction, then this would have been the governor of a small spring-wound music box with low torque. If the teeth are helical, winding around the shaft, then this would have been the governor of something with higher torque like a weight-driven cuckoo clock. The mating gear in a high-torque mechanism would have been at a right-angle to the axis of the governor. Wind-up record players used a completely different governor mechanism. Given the environment any ferrous parts would have rusted away.
Did Amelia's cosmetic case have a music box in the lid?
Is it part of a timer from some other device?
Otherwise, I would say it is a spinner from a fishing lure. Maybe a re-purposed available music box item.
That's a blast from the past!
https://tighar.org/Projects/Earhart/Archives/Expeditions/NikuVI/Niku6dailiesweek2.html (https://tighar.org/Projects/Earhart/Archives/Expeditions/NikuVI/Niku6dailiesweek2.html)
Dateline: Nikumaroro, 0530 Local Time, 3 June 2010.
"Another thing was found, and right now they are thinking that it may be part of a vacuum tube used for target practice by the Coasties. They're calling it the "dragonfly." I have sketched it based on Ric's description, which is a risky thing to do, but I did it anyway. In total it measures about one inch by one inch, and is made of brass or copper. The center portion is a rod, too thick to be called a wire. It has serrations on one side – not threads, but regular indentations. The "wings" are flat and thin, with holes as shown. An interesting piece."
(https://tighar.org/Projects/Earhart/Archives/Expeditions/NikuVI/dailiespics/dragonfly.jpg)