A large bead, measures about 28mm with a big 7mm hole (hard to measure exactly because of the rivet cap).

I posted it to the Asian Art Forums inquiring what the characters in the landscape scenes said, and was informed that they likely represent the Summer Palace in Beijing

万寿山, Wanshou shan (Longevity Hill)
昆明湖, Kunming hu (Kunming Lake)

And another AAF poster provided a link to another brass canister, altho the link mistakenly refers to the blue lining as "ceramic" rather than enamel.

I take back the speculation about Mandarin hat button use - that's ridiculous. The brass craftsmanship is pretty low, with sloppy soldering.
I guess what made me think the finial started out as something else is the mount. It's copper, not brass like the box, and looks as if someone took two stamped copper disks, cut out the centers, pressed them into bowl shapes, and sloppily soldered them together. They retain stamped images - swallow wings and tail, plum blossom branch, leaves, characters.
Messed-up leftovers from stamping furniture fittings, or what?