Becky, my knowledge of the Teares, Ballawhane, Andreas comes not from my own research (at least not in this period, though I have done some 20th century work), but from a family tree drawn up by Robert Evans Creer, a descendant of this family. On that tree there is no William, but there is a Philip Teare (1795-1864), about whom he writes:
“Philip Teare, 1795-1864, went to Bolivia in early life, and progressed until he became owner of silver mines at Corocoro near Takna (Arica was the port) in Bolivia, and made a lot of money and retired to Ramsey, purchased Moorehill, near Ramsey, which he re-named Bolivia Mount , married about 1854. While in Bolivia he had sent home for his nephew John Hugh, a lad, brought him up and promoted him, and finally left him the mines when he retired.”
REC notes that PT married a Corlett and had one son, PT junr. (1853-1875).

One needs to treat these Creer trees with caution. They are probably compiled from personal knowledge and memories of what family members told him. The only other Philip Teare on the tree is Philip, Liverpool, sailmaker, 1800-1860. He had a son William, about 1838 to 1862, single. So neither of these would be your Philip. No mention of a Kneale.

This is about as far as you are going to get using other people’s work. To get any further you will need to make a thorough study of Teares in Andreas, using the parish registers and censuses to start with. Andreas has the greatest concentration of Teares. There will be many different lines, and they will need sorting out, giving particular attention to farms and other locations. I have always done such work in Douglas, but I am guessing that you are in Ohio, and are not able to come over and put in the many hours necessary for this task. There are others who post on this board who are able to do these things at a distance, and they may wish to suggest methods.

This is probably about as far as I am able to help you, except to say that if you do not already have it, you should obtain immigrant William Teare’s death certificate in Ohio. It could well contain much useful information.