How to create two search results templates in themer

I need to create two different search results archives on a site. One so that when people search for products in the online store it returns relevant products, and one so that when people search for more general content on the site it returns the relevant posts / pages etc.

I’m using Beaver Build, Themer, WooCommerce, SearchWP. For the life of me I can’t figure out how to create two separate themer layouts for each search scenario. If I create a themer layout for search results then it uses that template for both the main search function, and for the store search function.

So for example, when I’m searching for a term from the shop the results are returned with this url format:

…/?s=[searchterm]&post_type=product

And when I search for a term from the main website the results are returned in this url format:

…/?s=[searchterm]

So the question is how to create a themer template that applies only to search results where post_type = product. Presumably I need to add in an exclusion rule in Themer Layout Settings so that I can create two themer layouts for search results, but I can’t see what relevant rule I can apply.

Am I missing something obvious here? Has anyone done something similar to this?

Thanks for any insights into this!