Inline Advanced Search

Hi all

Currently I have the Advanced Search Widget on my homepage : https://beta.koopkarre.co.za

I want to create a search box that looks like this : https://www.rawson.co.za/

I have tried to find the files in the theme directories that relate to the advanced search widget and how it is displayed in HTML but I have had no luck.

Any ideas of where to tweak this?

Thanks!