Is there any way to favorite a specific search tags? If not, would it be possible to implement the ability to favorite search tags?

none that i know of. it'd be a nice feature though. add it to the trac. i'm seeing this work much in the same way as the my-tags list.

What exact functionality do you have in mind? You can always bookmark your favourite search queries in your browser for quick access, if that's what you're after.

Even faster than that, you can set up most browsers to use custom search engines. For me, searching any tag string is as simple as typing "gb tag1 tag2 -tag3 user:someuser" etc. into my address bar.

I personally prefer to have everything linked to my Gelbooru account, than saved to my bookmarks. To top it off, a feature like this gives one's account more functionality.