Custom Taxonomy Template file not being used

I’ve identified the error of my ways, it was down to a misconfiguration and a misunderstanding.

Firstly, the archive-{post-type}.php file was not being loaded because the ‘Has Archive’ option for the custom post type was set to false. It worked the second I flipped that.

Secondly, I was under the impression that the taxonomy-{taxonomy-name}.php file was used to list the terms under the taxonomy, that is not correct. That is specifically for using a custom template for a post under that taxonomy.

It usually always is something simple. If only I’d just waited a bit longer before asking the question. Though sometimes, trying to work it out while you already have a question on SE seems to spur me further to work it out before someone else does!