Search will return as many results as you have set to the amount of posts you have set per page in your options. Default it is set to 10. Your extra results are found on
http://www.texburgher.com/search/writing/page/2 . This is completely similar to how tumblr manages regular pages.
The gist of search pages is this:
Search page is like a regular page, except all you do is filter for a certain word or set of words. Eliminating other posts. All the extra search page block does is add a couple of lines that you wouldn't show on your regular page to give information, like if there are search results and how many. You implemented it correctly.
Long story short, your search results are paginated in the same amount as the amount of posts per page you have set for your blog.