Shortcode for custom search (by a meta field)

There is only the one shortcode: [userlist]

In that case, what modifications must be done (besides adding search-author.php and adding the other piece of code to functions.php) so that the new search by custom field to appear?

At the moment, on the page where the shortcode is inserted, I still have the old search, the search by name.

Sorry. Solved. I was putting the search-author.php in the root folder of the plugin, not in the templates folder. My bad.

Glad you solved it. The basic how-to for customizing the templates is covered on the main plugin page: https://www.ads-software.com/plugins/simple-user-listing/

Also, I’m curious of something. Is there a way to search through two custom fields, and not just one?

Yes it is possible. You just have to manipulate the user query arguments appropriately.

For future readers, setting up a search by a meta field is covered in the FAQ.