John, it's obviously a conflict with an ext.(-s). Read the troublshooting sticky (link in my sig). Post errors if you see any related to any ext.
Yes, that I know. It may not be overly difficult to find the culprit, given that the latest example of the TMP problem arose after I had disabled the first six extensions; the fifth and sixth extensions are showing as being incompatible.
As I had, earlier today, created yet another profile, the one where I found that TMP does change the tabs' background colors, I'll start installing extensions one at a time; first, I'll need to install Nightly Tester Tools so that I can get numbers five and six to work. After restarting Firefox, I shall disable each one in turn. With any luck, extension five or six will likely be shown to be the causative agent.
Of course, I may find more extensions that also are fouling up the works, sigh.
[Update] I have now installed fourteen extensions, none of which, having been disabled and then re-enabled, have caused TMP to fail. More than once, I've disabled/enabled the first six extensions, and that, too, does not cause any TMP failure.
Incidentally, when the TMP New Tab button option is greyed out, the Customize button is still active, but clicking on it takes one to the Firefox customization pop-up module.
[Department of Lack of Progress Report Department] Thirty-five extensions installed, every single one disabled and re-enabled. TMP continues to work correctly.
Next step will be to start installing extension databases, cookie files, etc. into latest Firefox profile, continue to test.
[Here endeth ane tale of woe] As I wrote just above, I started adding in the various databases. The very last one added was my Stylish database; as soon as I started FF, the TMP background colors disappeared; I'm not sure if the "Open New Tab" button was still there. I next disabled all styles, which did not restore TMP, so I removed the Stylish database. When I restarted, I was quite pleased to find that my TMP background colors were reestablished, albeit one I had chosen--to make it quite obvious during all the testing--was still quite hideous.
I believe I've got everything set up in the current profile, but even If I don't, given that it is quite obvious that something in my styles collection was fatal, I don't believe that adding any further data will cause problems.
I finally removed the Stylish database from the profile that was not showing tab background colors, but evidently that profile was too badly damaged to use.
This process has been nearly as challenging today's Sunday New York Times crossword puzzle!