I have never tried to use the same volume for a TM backup and a external Photos library, but since you are having a Permissions problem in setting the Photos library location then it seems you need to be able to change the Ownership.so if I want to use it for a backup Im out of luck? Its no ig deal as Im using it mostly to save pictures to. I have never shown them when they were on my PC as I also keep them on my phone and iPad. I show them on TV with Apple TV and my iPad.
You could try and go to the TM System Preference, disable (uncheck) "Backup Up Automatically" check box. Then click the "Select Disk" button, select Glyph in the Backup Disks, and then click the "Remove Disk" button. Now see if you have the Ignore Ownership button with Get Info for Glyph. Can you set Photos app to use the Photos library on Glyph now?