I think I found the answer. In your Searches, reports, and alerts, go to Edit > Advanced Edit >
change "alert_type" from "always" to "number of events".
set "alert_comparator" to "greater than"
set "alert_threshold" to "0"
Save and schedule your search (if you haven't already). At this point, you should be able to click Edit and see "Edit Alert" and the saved search will show up under the Alerts filter at the top instead of Reports
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