Haha, I was in the Fortran club in Jr. High School. Punch cards. Good times. But back to your question...

The first step is to set Windows to show hidden files and folders:

https://support.microsoft.com/en-us/help/14201/windows-show-hidden-files

Then in your backup -- I'll call it the E drive but please use whatever is relevant -- you can click down this path:

E:\Users\username\AppData\Roaming\Mozilla\Firefox\Profiles

At that point, you might see one folder with a partially random name (like a1b2c3d4.default) or several folders. In the case of one folder, double-click into it. In the case of several, you can try each one.

Within that folder, look for a folder named bookmarkbackups which should contain files with dates in their names. For example:

bookmarks-2018-10-14_6178_gibberish==.jsonlz4

Copy a copy couple of these files to your new Windows desktop (not the old desktop in your backup) for easier access.

Next, to apply one of those backups to your currently running Firefox, you'll use the Restore feature. On the Restore menu, the bottom item should be "Choose File..." and that will let you point Firefox to the desktop to get your old backup and load it.

Steps to get to Restore: Restore bookmarks from backup or move them to another computer

Success?

Yeah - punch cards. I keep one to show the younguns, who are mystified by it. It's like displaying a Neanderthal artifact (which I suppose it is!)

Show hidden files and folders - that works. Searched my saved C: drive (where I keep Windows and program files); haven't checked D: (data files)

Three username folders - Default\AppData\Roaming\[no Mozilla, only Microsoft] - defaultuser0\AppData\Roaming\[no Mozilla, only DropboxOEM & Microsoft] - Gary\AppData\[no Roaming, only Local]

So ... no success so far. I've been good with keeping backups, but haven't specifically backed up Bookmarks.

sorta ... Went to my Seagate Toolkit and searched for "bookmarks", which took me to a series of April 2018 files. I guess that's better than nothing, but I've bookmarked a lot of locations in the past 6 months. Also searched the backup file for jsonlz4 files, got the same dates.

So it seems that recent bookmarks are lost, even though I backed up my entire C: drive. I'm puzzled by this. Why did it stop backing up bookmarks then? I thought (based on the article you suggested) that "Firefox automatically creates backups of your bookmarks and saves the last 15 backups for safekeeping."

If your software backs up the entire C drive, it should pick up the path

C:\Users\username\AppData\Roaming\Mozilla\Firefox\Profiles

Is it doing so now?

That is where Firefox keeps its data, including bookmark backups.