No, CJA automatically determines if a binding event is required if the dimension and the binding dimension exist at separate levels of your schema hierarchy. But there aren't any settings to require them on the same event or both to be within the product array.

Hi @PatrickJa6! Happy to try help to provide some details.   For your #1 scenario, if the search_term and product.name are on the same event when the search occurs, you likely just need to set your persistence for search_term to have binding dimension set to product.name along with the binding event...