Figuring out why an external USB hard drive won't spin down on my Mac

I am using a 2011 Mac mini as a backup server for all the data I store on iCloud, and for the first few days while I was setting up the Mac, I noticed the 4 TB and 2 TB external USB drives I had plugged in would spin down after a few minutes, and I would have blissful silence as long as there wasn't an active operation on that Mac (which should be fairly rare; just hourly Time Machine backups and periodic SSD activity since the iCloud libraries are all on SSD).

However, after a few weeks, I noticed that at least one of the two hard drives runs continuously, 24x7. Something on the Mac mini must keep hitting the drive and preventing it from spinning down.

To see what was happening, I used sudo fs_usage | grep VOLUME (in my case, VOLUME is 4\ TB\ Utility) to monitor what processes were accessing the drive, and what files they were accessing. After a few minutes watching (and doing nothing else on the computer, to make sure I wasn't causing any extra filesystem seeks), there were a couple regular culprits: