The search feature consists of the search form page AND the search results page. You as the admin can control what fields appear in each. You would do this within the following admin tool:

LISTING SETUP > FIELDS TO USE

And if you have category-specific field configurations you would do the same within those configurations. Look to the following screenshot of that admin tool for more:

Within that screenshot you'll see the location in the admin tool of the above tool. Within that you'll also see the "Display in Pages" tab location to click to see the search form and search results field configurations. Within the right side of that screenshot you'll see the "Search By" column which controls the fields that will appear in the search form. Click the checkbox of all fields you wish to appear as search criteria in the advanced search form of the software. Next to that you'll see the "Search Results" column. You would put a check next to fields you want to see within the search results.

Do note that each section of field type within the above admin tool have the same search form and search results configuration for the fields within those sections. See the following screenshots that describe those.