In /Users/browno/Library/Application Support/MobileSync Create a link "Backup" to point to your external drive
You'll need to move your Current "Backup" folder. I moved mine to the external drive as "Backup.ios"
Here the link in my /Users/user/Library/Application Support/MobileSync
lrwxr-xr-x 1 user staff 33 Jan 11 13:40 Backup -> /Volumes/EXTERNAL-5TB/Backup.ios/
I found a few examples online also:
Give me some space.
www.imore.com
I've been doing this for years and it saves a lot of space.