I can pin the secondary icon to the taskbar and delete the primary, but when I run FF from the new icon, it opens in safe mode.
Here's what I see (and get) when I pin the new running icon to the taskbar and delete the old one.
Here's a screen shot after I:
1) shutdown all running instances of FF
2) unpinned all FF instances
3) searched progams and files for FF
4) right clicked the search results and pinned the normal (not the safe one) to the taskbar
5) left clicked the FF icon in the taskbar... which generated a running program icon at the end of the list
6) rt clicked the running icon and pinned it to the taskbar
7) unpinned the original FF icon which resulted from step 4
8) moved the new and running icon where I wanted it
9) Rt click to start another FF window and only have the safe mode as an option, as per the image below.
Edit: as an interesting aside, if I go back and search for FF again and pin the normal mode FF, it appends it to the end of the taskbar list, as expected. Now when I left click on this icon, it appends a new window to the earlier icon I moved beside the TBird icon. It still refuses to add a new window to this icon. And there's no option to close the window from this icon either.