Automatically update desktop background when underlying image file is modified

Solution 1:

When you set a background from a custom graphic, a copy of it is created in your .local/share/backgrounds folder. That copy is being used as the background. You therefore need to modify that copy to make it work.

The desktop will automatically update if the file is modified in place or if another graphic is copied over the file (cp <another_graphic> <yourbackground>), i.e., provided the file inode does not change. Deleting the file or moving it, and then rename another will not work: your background will turn black. Only setting it back using the settings or logging out then back in will restore it in that case.