You can get to the Search Job Inspector by going to the lower-right of the search bar and clicking on the icon with a lower-case "i". If you click on that after running your search, you will find a breakdown of your search. Amongst the information in the report is duration.
runDuration is what you want to get the full time that the search took. Toward the top of that report window (Execution costs), there is a further breakdown to see where time was spent during the search, which can help you to optimize your searches.
There is of course additional information in the referenced search.log file, in case you need to refer to the raw data that the report is drawing from.