Analytics tracking for AEM Search

You can use getPageLoadTime plugin to measure the amount of time the page takes to completely load. check below link, in reports you need to filter by search results page.

https://docs.adobe.com/content/help/en/analytics/implementation/vars/plugins/getpageloadtime.html

If you want to measure time only search results then you need to do customization at your code level, usually in AEM to get search results we write servlet and make a request to it via AJAX call, you need to write java code or javascript code to find out page load time and pass it to your custom analytics search event, something like adding a new javascript object.