how to access photo library on the time machine back up

To test the backup of your Photos Library you have to restore the library from Time Machine. Photos cannot open the library as a part of a Time Machine backup. It cannot even open a Photos Library, if it is on a Time Machine volume.

You could restore the library to a different drive, so you do not overwrite your current version of the library.

To restore the library from Time Machine: (Use Time Machine to restore deleted files or older files - Apple Support)

• Connect your Time Machine volume
• Connect a second volume with enough storage for your Photos Library
• Select your Pictures folder in the Finder (the folder, where your current Potos Library is stored)
• Launch Time Machine
• In the Time Tunnel display select your Photos Library, ctrl-click it, then select "Restore to..." and select a folder on your second drive as the destination.

One the library has been restored to the second drive, double click it to open it in Photos and test it.

Now double click the original library to switch Photos back to your current library.

There is no clear answer of how to verify that Time Machine backups are being made. The Photos library won't open in Time Machine, as you have found.

The surest way to confirm that your Photos Time Machine backups are being made is to restore your Photos library and open it and check. I am not sure if you restore it to its original location whether it will overwrite your current Photos library. So I would restore it to other than its original location, perhaps to an external drive.

If your Time Machine backup is on a network drive, you can pull down the menu from the Time Machine icon in the Menu bar while holding down the Option key. The menu will have an item called Verify Backups, but it will be grayed out and not available if your Time Machine drive is directly connected to your Mac.

Also, you can do a first aid check of the Time Machine drive to see if any problems, and if there are any you can repair the disk like any other disk.

You can compare the size of earlier Time Machine backups with your current Photos library size as a rough way of confirming that backups are being made.

-- Rich