Becka, sorry to get back to you so late. My source for Thomas's father is_A History of the County of Lancaster: Volume 8_, pp. 232-237._A History of the County of Lancaster_ is part of the Victoria County Histories and can be found on British History Online.They are edited by William Farrer, whose name appears on just about every other record book for Lancaster.So far I've found that this series is well researched and correct.
You can find the research I've done for the Tunstalls on my web page starting with Alice, wife of Thomas Parr at : http://cybergata.com/roots/1095.htmhttp://cybergata.com/roots/1095.htm
At the moment, I'm reading Farrer's _Final Concords of Lancaster, Part I_, and his says that Akaris de Austwick's likely father was named Ughtred who was the son of Gamel de Austwick.
I live in New Mexico and teach New Mexican History, and the name Tunstall is a famous name in our history.A man named John Henry Tunstall came from England to became a rancher in Lincoln County in 1896.Tunstall took William Booney, alias Billy the Kid, under his wing so to speak, and Tunstall was among the first people to be killed in the Lincoln County War.