Success! Many thanks, Trevor. Although… I think I will have problems down the line as I am supposed to have a standard search on the site too, which will also be directed to the same Themer layout. Maybe there’s a way within Themer to assign it to a particular search. I’ll run that past the Beaver support guys.

Ok, I’ll explain, for the benefit of others:
I have a search and filter pro instance on a Beaver Themer archive layout to search custom posts. Originally I had it targeted (called ‘location’ in Themer) to Post Archive pages for that particular custom post. That worked for every instance except when a search didn’t find any result. Then the message came back in a blank page and not in the Themer layout. Frustrating, because it was 99% working.
The trick was to tick the “Force is_search to always be true?” checkbox in the advanced settings on my search form (in S&F Pro). I then found that I didn’t need to target the custom post archive but just the search results.
This works for my situation. However, there isn’t an option to target a particular search in Beaver Themer (as far as I know… and I’ll be taking this up with the BB support). This will cause a problem down the line when I want a regular search on the site, which we have promised the client. With this setup, any search will be displayed in the Themer layout for my custom post, which will not be relevant in other situations. Hope that makes sense… difficult to explain.

My other issue was that I wanted the search to search inside the custom post which has lots of custom fields. Trevor pointed me in the direction of Relevanssi, which adds the functionality of being able to search inside custom fields. There were a couple of settings that needed configuring to get it to work properly. I had to tell it to look in the Custom Post Type I had made and I was also able to list the fields I wanted it to look in.

I’m not all that technical, so I hope that makes sense and helps someone else.