As of posting the enigmatic-puzzle tag has this minimal usage guidance:
Puzzles where the genre or solving strategy of the puzzle is not explicitly stated; puzzles where the puzzler must deduce what type of puzzle it is.
But there is no further explanation or information about this tag, and it's intended use.
If you look at this SEDE query, you can see the top 5 tags without a wiki:
That the enigmatic-puzzle tag is so widely used, without a good usage blurb and no further wiki information, is slightly troubling.
It causes the tag usage to vary wildly, and (anecdotally) in the worst cases encourages making questions obscure for the sake of increasing the difficulty rather than making them better puzzles (evidence by the fact I've seen some enigmatic puzzles get highly upvoted, only to nose dive once the 'trick' of solving is revealed).
Here is a suggestion for the sort of thing I'd like to see in the usage guidance, partly based off of this answer:
Use this tag when the solver's first task is to determine how to solve the puzzle. Merely omitting information on how to solve is not sufficient to justify using this tag, and an enigmatic introduction or pseudo-explanation is favoured.
However I'd still like to see answers discussing how to improve on that block of text, and what to put in the wiki-info for the tag. Preferably we'd list some good examples, and also some more information what makes a bad enigmatic-puzzle, i.e. what to avoid.