No user library back up on Time Machine

Time Machine does back up the User´s normally hidden Library folder, including the Mail folder that contains everything relevant to Mail. But you have to have the User´s Library folder visible and selected in a Finder window to be able to find it in Time Machine. In case you're not sure how to do this:

Click on an empty spot on the Desktop to activate Finder and make it the frontmost application.

Now hold the option key down and click the "Go" menu in the Finder menu bar. Select Library and a Finder window will open showing the contents of the normally hidden Library folder.

With the Library folder still selected open Time Machine from the upper right of the Finder menu bar. You can now select to restore the Mail folder (it may take a few seconds for everything to appear). I've just checked that this still works in macOS Mojave on my iMac...it does. Hope this helps you! Regards, Ian.

Hi Chris! This is a very long shot, but it´s all I can think of doing for the moment, and it´s what I´d try.

Eject the external drive you use for TM backups and then disconnect its USB cable from your Mac. Re-boot your Mac and then re-connect your TM drive. Try opening your User´s Library in TM again. I do hope the might help! And to make sure this problem doesn't occur in future do check TM´s exclusion list in System Preferences > Time Machine > Options (bottom right). Regards, Ian.

You're welcome! Sorry for nor replying sooner, Chris, some virus knocked me off my pedestal!

I assume you mean a locked library folder, not a file. No matter, this might mean your User permissions are somehow not set right. Select the file/folder and type Command + I to get info on it. Down at the bottom of the Info pane that opens check that you have read & write permissions. If not, click on the padlock to open it and set your permissions so that you can read & write. Close the padlock. This should now allow you to access and interact with it. Otherwise I really don´t know what else to suggest at the moment. BTW, what you suggested about saving the Mail folder in the User's Library separately is a very good idea, and is something I got into the habit of doing some years ago. I do this about once a month. I do hope that some more knowledgeable forum user reads your post and has a solution for you. But I have a feeling that Apple Support were probably right when they confirmed that your mailboxes had disappeared…☹️ How about contacting your service provider about your lost mails? Might be worth a try. On my provider's website I can access mails going back to 2010, when I switched to them (German Telekom) Regards, Ian.