Don't force eject. If it wasn't potentially harmful, it wouldn't be a "force" operation.
We're not doing anything that would keep a drive busy. When we finish, we have nothing "active" on the drive. The only thing that makes sense is either Spotlight or Antivirus.
You can try to check, if you're comfortable with Terminal, using the "lsof" command. You'd run
Code:
sudo lsof | grep "The Backup Volume"
substituting appropriately for "The Backup Volume" (retain the quotes). That would give a list of all the files open on that volume, and the processes keeping them open...