There are quite a few questions about this and the answer usually involves symbolically linking the backup file to the external drive. (E.g. Is it possible to backup iOS devices to an external drive? or Backup iPhone to external drive on Mac)
The command I ran was
ln -s /Volumes/<externaldrive>/iOSBackup/Backup /Users/<username>/Library/Application\ Support/MobileSync/Backup
But when I try to backup, I get:
To save space I stopped doing local backups a long time ago, so there is no backup in my Mobile Sync/Backup folder to begin with which may complicate things. When I go to Devices Preferences, there is no backup to delete (as expected):
It appears that the symlink process no longer works (the questions all seem to be from 3 years ago), or perhaps I've not done it correctly.
Best Answer
Edited to remove a wrong suggestion.
I have not witnessed any problems making backups while symlinking the MobileSync/Backup directory, but I have seen many problems restoring the backups with the symlink setup. With that said, it's possible the issue extends to making the backups now too. That would be interesting to verify.