I know many people have complained about being unable to eject a Time Machine disk. The usual response I have found online is to download and use "What's Keeping Me?" to find out what process is accessing the disk. Well, I have done that, and it turns out the culprit is mds_stores -- in other words, Spotlight.
Now Spotlight shouldn't be indexing my Time Machine volume -- I have it excluded in the Spotlight privacy pane. Killing the mds_stores process allows me to safely eject the TM disk, so in a sense my problem is "solved". But why is this happening?