Boy, do I have news for you :) ; will repeat an f/t/F/T motion forwards, and , will move back. Having it separate from n/N means that they have a separate history and you can combine them to repeat motions.
It’s IMO easier to hit f again than to reach for the semicolon, and moreover this frees ; and , for usage in your own mappings (e.g. leader and localleader)
The only issue is (content warning: controversial remap) I have ; nnoremap'd to : and : to ; so it would be awkward to advance multiple matches. I would hate to lose my one key :, but perhaps there is a workaround if f is useful enough (for those unfamiliar, with / or ? you use n to go to the next match).
However, I'm using Doom Emacs these days (with evil, of course) and while it emulates vim's command mode with colon, it's designed to drive most "commands" with space as a sort of leader key. I could imagine space being a nice remap for : in vanilla vim since it does nothing in normal mode.
Now, turning to doom-emacs, SPACE is the modal for getting the list of next available commands. To save a buffer in doom-emacs I use SPACE w SPACE. Et voila, the same muscle memory works for both. BTW I also set up :ww to write/quit so SPACE W W does this in both editors. Well, it works for me!
The only downside for me, and I've been reluctant about this for years, is I ssh into a lot of Linux machines that usually just have the standard stuff and default configs. This has kept me from experimenting with a lot things so as to keep my muscle memory also standard (thus avoiding i.e.: zsh, extensive .vimrc with plugins, etc).
When I played piano there was a point where I could play a piece without thought but couldn't parse the sheet music or know what my fingers were doing anymore.
As I just learned browsing through the book linked in this thread, there is!
Use ; to go to the next match or , to go to the previous one.
Great find.