Hi Georgia,
Thank you for the details, it helped a lot.
The main difference on the two search bars was, that the one on the linked page is using the Regular engine, while the other one the Index table engine.
I found, that the the word “conductor” was actually within a custom field, which was not indexed, hence the results were missing from the header search. I selected the following fields in the index table options panel, and created a new index: https://i.imgur.com/Yv5YiNS.png
That seems to have resolved it. Now I am getting those results as well: https://i.imgur.com/5aa9Nud.png
