This works for Gmail's search results and when you click one of the labels. For example, you can go to the "All Mail" system label, click the pagination message, select "Oldest" and find the first messages from your Gmail account.
For the search terms that return a lot of results, the only pagination feature that works is "newest" because Gmail shows vague estimations for the number of results like "1-20 of hundreds" or "1-20 of thousands" and it can't determine the last page of results.
{ Thanks, jpp. }