The Book of Briars is being opened communally, by everyone. After we succeed in finding four fragments and completing a magimystic assessment, a new key is found and a lock opened. Right now we've unlocked two locks - the flora and fauna locks - and we're currently on the third.
I'm not sure why the locks wouldn't be showing, it might have just been an error of some sort, or perhaps magimystical currents weren't right. Either way, there definitely should be two of the locks unlocked, on the left side of the book.