Custom Taxonomy template is not recognised

I cannot get the archive to show for the taxonomies

And in the comments you said:

I can’t get to example.com/lips

And similar to what I said here:

  • Taxonomies, unlike post types, do not have an archive page (which displays posts from all terms in the specific taxonomy), so it’s normal if you “can’t get to” example.com/lips or example.com/eyes, i.e. example.com/<taxonomy key>.

  • And secondly, taxonomy templates like taxonomy-lips.php actually rely upon the current taxonomy term, i.e. there has to be a term being queried in order for a taxonomy template to be used, and for functions like is_tax() to return true. So remember, the query determines the template and not the other way round. And for example example.com/lips/category-slug worked (i.e. taxonomy-lips.php was used) because there’s a term being queried which is the one with the slug category-slug.

So no matter how many times you flush/regenerate the rewrite rules, taxonomies simply do not have an “all-terms” archive, only specific terms in the taxonomies. See @bosco‘s answer here if you’re interested in knowing more tech stuff about taxonomy’s “archive page”, which by default do not exist or not implemented in WordPress core.

I hope this answered your question, and if all you wanted to have is for the example.com/lips and example.com/eyes to display posts from all/any terms in the lips/eyes taxonomy, then an easy way is:

  1. Create a custom Page (post of type page) and give it the lips or eyes slug.

  2. Assign a custom page template to that Page.

  3. And then make a secondary/custom WP_Query query in that very template.

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