Thank you for the details and kind words!
I've looked through the setup, and the problem is that those custom fields does not actually store the author name, only a reference ID (relationship) to it – because it's a complex ACF custom field, not text based. The actual author name is stored somewhere else, most likely in the options table in the database or somewhere in ACF internally. This means, that it's impossible to search through, as the actual data is not visible for Ajax Search Pro in the options meta database table.
If there was a quick code based solution, I would gladly look into it, but in this case there is nothing I can do to make those fields data available for the search query.
In these cases I usually recommend 2 possible solutions:
1. creating a simple custom field on the post editor, for example with the name “search_keywords” and writing every extra required information there – like author name, tags, places etc..
2. ..or to enter the additional information as post tags, however solution 1. is more transparent, as it's not visible to the user.
Then on the search options select to search the “search_keywords” custom field as well, and done.
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