This is no help to you, but... I can see them on Windows 7. They are quite narrow. I can click and drag them if the "middle finger" of the hand is over them. Not sure whether it is possible to do that "blind".

Your toolbar customizations are stored in the localstore.rdf data file in your currently active Firefox profile folder. This XML-based file makes difficult reading and I don't recall seeing any good documentation on how to edit it. If you want to give it a try, please make a backup first.

If the file becomes corrupted (or more corrupted, as the case may be), you can rename or move it and Firefox will generate a new one with default settings, and you can start customizing from scratch.

With that out of the way, it actually looks as though you should be able to find and remove the separators.

  <RDF:Description RDF:about="chrome://browser/content/browser.xul#addon-bar"
    mode="icons"
    collapsed="false"
    currentset="addonbar-closebutton,stylish-toolbar-button,spring,downloads-button,separator,fireshot-Capture-Button,greasemonkey-tbb,noscript-tbb,fiddlerhook-toolbar-button,status-bar" />

To give this a try:

Open your current Firefox settings (AKA Firefox profile) folder using

Help > Troubleshooting Information > "Open Directory" button

Switch back to Firefox and Exit

Pause while Firefox finishes its cleanup, then make a backup copy of localstore.rdf (e.g., localstore.0808) and open the rdf file in a text editor to find and edit the separators out of the addon bar.

When you restart Firefox, your changes should be evident.

Any luck?

I think it worked. When I restarted Firefox, it upgraded to version 23.0, so that could conceivably be part or all of the solution. With this new version, the Classic Compact theme that I use was diabled as incompatible. I can now see the separator bars and manually move/remove them. I'm guessing that the bars were not visible under the Class Compact theme. But in any case, I had already edited the localstore.rdf file and the extra separator bars I deleted from that file no longer appear in the Add-on Bar. Thanks for your prompt and useful reply!

It was not possible to remove the separator bar "blind" in the way you describe. I had already attempted that numerous times.

You should see the separators in the Bookmarks/History Manager (Library; Bookmarks > Show All Bookmarks).

You can consider another Linux theme and/or icon pack that shows the separators more clearly.