Hi @blakespot
If he doesn’t use PHP code nor the Local JSON feature, then there’s nothing else I can help you. The best way to find it is to ask the original developer as he can do anything he wants, and we wouldn’t know about it at all.
Also, please keep in mind that you can set different place to save the JSON files. This page should give you more idea about it: https://www.advancedcustomfields.com/resources/local-json/#saving-explained.
Another thing you should check is if he used a plugin instead of the theme to add the fields. In this case, you can try to check if the fields show up on one of the WordPress’ stock themes (like Twenty Sixteen) with other plugins deactivated. If it disappears, then you can activate the theme and plugins one by one to see which one that adds the fields.
I hope this makes sense 🙂
