Hello
Tuttle - not sure that I can be of much help, but please tell us whether you using a Mac or PC computer and what OS is running on your machine - likely makes a difference as to potential solutions of your backup problem(s).
For myself, I have Mac computers, so some of my thoughts may be of no use if your on a PC, sorry. How much free storage do you have left on your computer - I'm assuming that is really not an issue? Also, how many iDevices are being 'backed up' to this computer? If you're on a Mac (if a PC then you'll have to google), the backups are kept in your 'user library' (see that attached image - I've 'drilled down' through my user library to where the backups for my iPad Air 2 are kept - seems to be just two) - how many folders are in that location which might be a consideration.
Also, in trying to save your backup to an external HD, are you sure that iTunes was doing the procedure correctly and not just reporting the 'lack of space' from your computer's drive? I just say that because in reviewing this
osXDaily Article, there appear to be a LOT of steps in setting up an external drive at least in OS X.
Finally, are you also backing up your iDevice to the cloud? I use iCloud as my main 'daily' backup and then about once a week will also do a backup to my laptop. Dave
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