You are welcome!
Well, the archive pages are not controlled by the search, those are automatically generated by WordPress and then handled by the theme.
While this is out of my support scope, I will try to help you out.
It is possible to hook into the query and probably make them first via the pre_get_posts hook. I have also found this plugin, you can try it, although that may conflict with the actual search query.
It might be better to have it custom coded though, this shouldn’t be difficult at all, and then you don’t have an additional plugin to take care of. I suspect it’s probably a few lines of code only to change the archive queries. I usually recommend this service for customizations and code requests, they are very professional and helpful.