You can not add this specific search on result pages, it will load on all pages or selected pages, because there is no separate result page/menu for this search.
Creating a Standard Joomla Module
Log in to your Joomla administrator panel.
Navigate to Content > Site Modules > Modules.
Click the "+ New" button to create a new module.
Select the SP Property Search.
Assign the module to a specific module position available in your template (e.g., "top1", "bottom", "sidebar").
Go to the Menu Assignment tab to select which menu items or pages the module should appear on.
Save and Publish the module.
Thanks