Most likely Spotlight Indexing is still holding onto the volume, but it could be any app that was used to access the volume. Sometimes you have to make multiple attempts to unmount volume or eject the drive before Spotlight or whatever process holding it will release it....other times you just need to wait for it to finish. There are a couple of command line options to unmount a volume/eject a drive or to view which processes are holding onto the drive.
You can use the following command to try unmounting a volume. If it is unable to unmount it, then it will display the ProcessID and name.
diskutil unmount <path-to-mounted-volume-goes-here>
Start by typing the command making sure to leave at least one space after "unmount ", then drag & drop the mounted volume from the Finder onto the open Terminal window in order to provide the proper full path to that volume. Do not type the part with the angled brackets since that is just meant to explain the command options.
Let's say your external volume is named "MyVolume", then the command would end up looking like this since external drives/volumes have their mount point at "/Volumes":
diskutil unmount /Volumes/MyVolume
Why are you risking your backups by adding a second partition/volume to your backup drive?
Are the files you are storing on that 2nd partition/volume important? Do you have more than one copy of those files?
If those files are important & the only copy, then how are you backing them up? I hope not to the same drive because if that drive fails you lose that 2nd partition and the backup on the 1st partition. And why do you want to put your backups at risk? You want those backups to be there in case of an emergency, but my making the drive more complicated you are increasing the risk of that backup not being there when you need it the most. Just because something is possible & can be done, does not mean it is a good idea to do it.
FYI, it is never a good idea to partition any drive. People almost always discover later on that one or both partitions are too small.....at that time it will be a huge pain to correct things. If you need to split a drive which is using an APFS file system volume, then it is best to create a new APFS volume instead which will act like a partition, yet not require any physical destructive changes, nor any commitments to sizing the volumes since they will both share the same storage pool, but yet remain separate.
Add, delete, or erase APFS volumes in Disk Utility on Mac
