Everyone knows that Google is the top search engine globally. Why not incorporate their search to cater to your blog specifically? You can add a Custom Search from Google to your sidebar in a couple of easy steps through your Google account.
First, go to the Custom Search Engine Page and click the blue "Create a custom search engine" button. You will be brought to a new page where you can add your blog link (ie: https://example.typepad.com or https://www.example.com) and blog name. You can add as many websites as you'd like.
Click "Get code" to view the code to add to your sidebar. In your Typepad account, go to Design > Content > Modules > Embed Your Own HTML - paste the code here, click OK and save your changes. The Google Search bar will appear in your sidebar.