Search on Engine Change is a great add-on. The functionality was recently incorporated into the new Firefox Search Box, but if you prefer to use the old Search Box you may miss the function from Opera where a search is executed when you change the search engine.
Search on Engine Change adds this feature but it has a bug which is described below:
If you have one Firefox window with some text in the searchbar and you’re working in a different Firefox window with no text in the searchbar, changing the engine in the second window will cause a search to be executed, even though the searchbar is empty.
I contacted the developer last year but since I haven’t heard back I’m uploading my patched version here. I’ve bumped the version number to 1.3.
To make use of this extension you will need to restore the original Firefox Search Bar using this preference in about:config:
browser.search.showOneOffButtons = false