Usually specific game characters don't get tagged with their game, this happens in hundreds of matara_okina posts (she doesn't always have the hidden_star_in_four_seasons tag) while in other games like for example dark_souls_2 most characters are always tagged with the game.
Is there a real explanation for this other than it is just that they do not show enough of the game to be tagged?
Examples:
Okina Matara posts:
post #3954435
post #3923232
post #3910406
(just searching matara_okina -hidden_star_in_four_seasons will give you hundreds of results like this)
Individual games tagged:
post #3868178
post #3869943
post #1800968
(searching any of these characters with -dark_souls_ii will lend no results at all)

Awedsy said:

Usually specific game characters don't get tagged with their game, this happens in hundreds of matara_okina posts (she doesn't always have the hidden_star_in_four_seasons tag) while in other games like for example dark_souls_2 most characters are always tagged with the game.
Is there a real explanation for this other than it is just that they do not show enough of the game to be tagged?

All Matara Okina posts are tagged Touhou, though. I guess Touhou might be a bit of a special case because the individual Touhou game tags are only used if the post has some kind of relation to the specific game, such as all (and only) characters from that game present in an image.

See topic #14159.

Going by the Touhou wiki:

NOTE: Due to most characters appearing in more than one game, only the "Touhou" tag should be used unless a specific game is directly referenced by the content of the post. All of the characters in a picture having debuted in the same game is not sufficient to constitute a direct reference. Depicting the full cast of a game (with or without the protagonists) will usually count as a direct reference, so long as no other characters are present.

If you're going to discuss this, a case should also be opened for Fate_(series).

Awedsy said:

Individual games tagged:
post #3868178
post #3869943
post #1800968
(searching any of these characters with -dark_souls_ii will lend no results at all)

I don't know touhou enough to speak for the specific character you talk about, but given Dark Souls 2 it's kinda easy to say where those characters come from. Even if the Pyromancer appears in ds3 it's not a recurring character there, but only appears once. The Emerald Herald only appears in part 2 and the armor is the most known for part 2. It's not exactly what you wanted to know, but the point is: You can only tag what you know and I guess most uploaders who upload Dark Souls images know those specific games. I don't think that darks souls and other games like that are specifically searched by a lot of users, which leads to, that the copyright tags are way more detailed.
Just compare the amount of all souls images with this character. The character alone has over 4 times more images than DS2.

On the other hand: Female characters are mostly uploaded even if the uploaders don't know the specific copyright. They won't tag anything they don't know anything about, as long as the main copyright is given.
For the rest, just look at the quote from MU.

Usually, entries in a video game series feature substantially different or expanded worlds and characters. The Souls series, to the best of my knowledge, doesn't retain much of the plot or cast between games, so it's intuitive to specify which game you want to see. The Touhou series has small, rapidly-paced releases that just append story arcs to the same universe in the way a manga would, so it doesn't make sense to forcibly separate the releases most of the time.

On top of this, Touhou is also known for having a huge segment of fans and fanartists who just don't play the games at all and treat the series like a shared doujin universe.

Mysterious_Uploader said:

If you're going to discuss this, a case should also be opened for Fate_(series).

I've thought of making a thread for that exact subject recently, actually.

I always tagged Fate posts with the same logic as Touhou posts; for example, I would only tag a post of astolfo_(fate) with fate/apocrypha and fate_(series) unless it obviously referenced Fate works other than the character's debut work, whether by environment or other characters present or outfit or etc. But I often come across Fate pictures that are tagged with a bunch of additional Fate works (usually at the very least fate/grand order + debut work) for no real reason other than, I'm assuming, 'this character is in FGO'.

Not tagged:
Super Smash Bros. was consolidated into one tag because of overlap, and there wasn't much point in separating by game.

Usually not tagged:
Touhou is similarly grouped together because of overlap. There's occasions where it makes sense, though.
Individual Pokemon can appear in any game or something so there's overlap.

Infrequently tagged:
Some sequels like Tekken 7. Tekken has more posts with 1 copytag than 2.

Sometimes tagged:
Someone from Street Fighter may or may not have a second copyright tagged.
Chun-li has more posts with 1 copytag than 2, but Han Juri has more tags with 2 copytags than 1.
They have distinct different appearances by game.

Someone like Utsumi Erise gets the F/GO tag because that's where her recent visuals come from.

Usually tagged:
Series entries like Dark Souls II, more distinct series entries like Star Twinkle Precure,
sequels that are also their own subseries like Final Fantasy VII, spin-off series like Idolmaster Million Live!

There seems to be some de facto guidelines and trends, nothing ironclad of course.
I guess what matters is, does it make sense?