By default, search is disabled for new external objects. However, you can validate and sync an external data source to automatically create external objects. Syncing always enables search on the external object when search is enabled on the external data source, and vice versa.
When Summer ’16 becomes available in your org, Salesforce initially selects the Allow Search option for existing external objects. However, if search is disabled on the associated external data source, those external objects still aren’t searchable. To include an external object in SOSL and Salesforce searches, enable search on both the external object and the external data source.