I do not recommend doing this.
The non-site information under your cPanel home directory is specific to the versions of cPanel and the various servers (e.g. Dovecot for email) running on the server. While these files can be backed up by setting the site's root to the cPanel home dir it's not a given that the backup will be restorable on a different server, or even on the same server after you update any of the server software.
Furthermore, restoration will be convoluted. You will need to use Kickstart from the command line to extract the backup archive and move the installation folder inside public_html. You will also need to restart all of the server's services for cPanel to see the new configuration files. Assuming it can even read them without erring out, of course.
Even if that is successful, which is really not a given at all, it would make it impossible to restore your site without at the same time restoring everything else on the account.
If you want to be able to clone or transfer the entire cPanel account you need to use cPanel's import and export features.
If you want to back up and restore your site you can use Akeeba Solo.
If you want to back up and restore just your email messages, bot email account setup or mail filters, you PROBABLY can backup up and restore the mail folder under cPanel – in this case you don't really need to use Akeeba Solo but if you do want to you can, using a custom site root and the Site Files Only backup type.
At any rate this is not something I recommend. It's hard enough to use a generic tool when you are the one who's set up the server and understand perfectly well the implications of your actions. It's nearly impossible when you're talking about cPanel which can be very different things depending on its version, not to mention that it makes design choices to abstract all the nitty gritty details of server software configuration. You can't be sure about the implications of your actions.
To put it simply: if you could do what you have in mind with tar and mysqldump you can do it with Akeeba Solo – much more automated, of course. If you're not sure if you could do it with tar and mysqldump don't try to do it with Akeeba Solo, your experience would probably suck and I wouldn't be able to help you.
Nicholas K. Dionysopoulos
Lead Developer and Director
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