Hi Sarah,
You can change the JS where the predictive search is called :
~\CMS\CMSWebParts\SmartSearch\SearchBox_files\PredictiveSearch.js
On line 105 you can change the timeout :
me.timeout = setTimeout(function () { me.CallPredictiveSearch(query, query); }, 500); // set call timeout (start the search countdown)
But the delay of the predictive search depends also on how low the search is taking so it is also related with the performance from your website.
Good luck with programming!!!
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