I definitely think that the more specific the tags, the better. The one catch is that we should probably keep the more general tags as well until they become unwieldy.
There's a limit of 5 tags per question - those should be the best 5 tags for a question. So if a question has 4 tags, feel free to add rook-endgame as an example. However, if it has 5 good tags already, then probably leave it.
I guess that new tags should arise "naturally". The other way to do it is to make sure every question has minimum e.g. 3 tags and maximum e.g. 5 tags. Then, new tags will definitely arise.
Regarding endgames, I think that the search engines on- and off-site will pick up a separate tag setup "knight" and "endgame". I am not a big fan of "knight-endgame" and similar tags. What is a knight endgame, is it a knight versus knight? How about knight versus three pawns? I vote for separate tags. Cheers.