Synctrain

With Synctrain you can securely synchronize files with other devices that have Syncthing installed. You can choose to synchronize full folders, or choose specific files. With Synctrain you can also stream audio and video files from other devices. When you synchronize files, all changes, including deleting files, also happen on your other devices.

Am I missing something here? If so, spool me up.

If I understand correctly, iOS apps don't run continuously in the background which doesn't match OP's 'automatic' requirement. But, I mean....tap the app, sit the phone down for a few minutes, and viola! Now if you are one to take hundreds of pictures daily, and you haven't backed up in a while, you might want to disable 'auto-lock' temporarily so the screen doesn't time out, or you can keep up with regular backups. iOS doesn't expose the photo library as a regular file system, so the app uses the system photo picker API to access new pictures, and you have to point Mobius to the DCIM folder iirc.

So, ok not fully automatic, might involve one or two steps depending on the time span between backups, but it would work. I just backed up 131 photos in less than the time it took me to type this comment.