From what I see is that searching within the Timeline executes a RetrieveTimelineWallRecords function. The FetchXml in here takes the search string as a like value for the subject and description of the activities.

Since users want to add additional information to activities, e.g. have a custom subject field on email to store their own subject text, please provide an option to configure which columns to query when executing a timeline search. Another option might be to take the setup of the search columns as defined in the related table's quick find.