In your profile.

https://support.mozilla.org/en-US/kb/profiles-tb

Specifically you want files with a .mab extension. But have you worked out how you'll use them?

Thank you. Two subsidiary questions, please:

(1) I am assuming, that if a computer user employs a typical mirror or image backup program to capture the entire hard drive, Profile would be included as a natural part of that backup and then restored along with everything else were a comprehensive restoration necessary to a new hard drive or computer. Is this correct?

(2) Selective restorations are usually possible using such a backup program, including the one I have. Is Profile the sort of item that would permit its restoration by itself, if necessary, even if aggregated with everything else on the hard drive in a backup, or would it be preferable to back Profile up separately?

Can I assume this is Windows?

1) If you're imaging the whole disk, or at least Users and everything below then yes you will capture the profile.

2) Thunderbird's Address Book is made up of subsidiary address books. Personal Address Book and Collected Addresses (represented, respectively, by abook.mab and history.mab) are obligatory and to some extent hard-coded. These two files could indeed be restored piecemeal into a new profile. Other files representing user-defined address books are problematic and cannot just be copied into a profile. You'd normally use an add-on to import them, which would have the beneficial side-effect of adding them to the index of address books.

If you backup and restore the entire profile then this problem doesn't arise because you're also restoring the Address Book index.

Some users get into trouble because they use Microsoft tools to make a backup and oddly, these tools don't always include the AppData/Roaming folders where Thunderbird places its profile. If the user is savvy enough to recognize this and add these folders to the backup then all is well. Some users tackle this by moving the data part of the profile to a folder which is included in the backup. However a small but critical part of the profile is the profiles.ini file which must be placed in .../Roaming/Thunderbird/... and so would still be overlooked by the backup process if using its default settings. Another (and IMHO misguided) approach is to move individual mailstore folders from the profile to somewhere in the user's personal directories, but this leads to fragmentation of the profile and a rather messy and unnecessarily complicated maintenance job thereafter.

What this boils down to is that the profile is a set of interconnected and cross-referenced files and therefore partial restoration, in general, is unlikely to be successful. A good backup program should be able to recognize changes and store the deltas, avoiding wholesale copying of everything and so make incremental backups quicker. But to be safe you need to restore the whole profile, including the separate profiles.ini file.

I should add that I can't see any need to backup the Thunderbird profile separately; a complete disk image or mirror should suffice.