I think I have found the reason. If I'm guessing right, then you had an older version of the search installed, where “Image Precache” was enabled. I left that code in the search in case someone needs it, but it cannot be disabled from the frontendt. Anyways, all you need to do is delete a few lines, and that empty 1,2s ajax request will disappear.
Open up the wp-content/plugins/ajax-search-pro/ajax-search-pro.php file.
Delete lines 232-250:
Clear your cache and CDN cache, and you shouldn't see that long request anymore.Best,
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