Ok I search Google and get some results which merit further reading. I right-click on one to get a menu, so I can select “open in new tab” BUT:
Sometimes, it just opens a new window on the right click, sometimes a new tab, sometimes the expected menu… What gives?
I have tried to widen the sensitivity of area under the mouse cursor to no avail…
This sounds like a well known bug. The workaround is to install this mouse gestures add-on. If you don’t want gestures, you can disable them all in the add-on (or if that won’t work leave one, but make it so obscure you’ll never trigger it by accident), and the overhead of the add-on should be fairly small.
wierd - glad you found a solution, BUT did you know that you can just configure Google to open clicked links in a new tab anyway?
Just click on Preferences and there is an option at the bottom to “Open search results in a new browser window.”, just make sure your Firefox preferences all force new windows to open as new tabs instead 
Thanks and ++reps to you both!