www.pivonka.com is a site established by an unrelated Pivonka for the benefit of his family. The site has been on-line for several years. Mr. Pivonka is a computer professional, and the site has a much richer design than this one!
Pivonka's in St. Mary's Cemetery, Manitowoc Co., Wisconsin This is an excerpt listing Pivonka graves in a cemetery chock full of Czechs, and includes direct links to the entire record and Manitowoc Co., WI genealogical resources. It is possible - based on the coincidental recurrence of given names for family members (Mary, Thomas, Leo, Clara, Frank, Lillian, etc.) in one of the Pivonka families here - that Jacob Method Pivonka's lost brother Thomas ended up in Wisconsin. Or maybe that's what Cxechs in the US were naming their children in the late 1800s and early 1900s.
http://www.pivonkafamily.com/ is the site of the Joe and Cathy Pivonka family of Illinois. I don't know whether Joe is from the KS, TX, or WI Pivonka group, or another group I don't know about.