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Try Vimperator add-on for Firefox. https://addons.mozilla.org/en-US/firefox/addon/vimperator/

Given enough proficiency, you will not have to use your mouse while browsing.

Firefox still has this feature, I believe it is referred to as "quick find" and is available with either forward-slash or apostrophe. You can follow a link with Enter and go to the next instance of the search term with ctrl-g or cmd-g.

Gif example: https://i.imgur.com/C2zH4CZ.gif

apostrophe starts quick find, but only searches link text. So in your comment, typing 'gif would only select the text in the link; it wouldn't find as a result the "Gif" earlier in that sentence.

And with either, F3 or C-g searches forward, and Shift-F3 or Shift-C-G searches backward. If you're on a link, Return navigates to that link.

I have this using the "Findbar Tweak" [1] add-on, it works with searching and pressing enter. You can also press / for quick search.

[1]: https://addons.mozilla.org/firefox/addon/findbar-tweak/