I read message #54723 by Pat at the New York Genealogy forum and I did not have the 1850 census with the parents of Eliphalet Terwilliger/Ephalet Terwilliger...
Portion of message by Pat at the New York Genforum.
"...I wasn`t able to find David in 1850. I did find a legal notice from an 1892 issue of the Auburn Argus newspaper that mentions David Terwilliger of Gratiot Co., MI. See below. Some of the persons mentioned in this notice are, I believe, shown in one Terwilliger family on the 1850 census in Sennett, Cayuga Co., NY. Benjamin Terwilleger42 Catharine Terwilleger39 Elisha Terwilleger16 Hellen Terwilleger14 Lewis Terwilleger12 Catharine Terwilleger9 Frances Terwilleger5 Benj Terwilleger3 Eliphlette Terwilleger2
..." end of portion of the message by Pat Source: Message #54723 at the New York genforum page, a message from Pat in reply to David Terwilliger.
Message #785 posted on this forum has the same legal notice and ELIPHLETTE TERWILLIGER was spelled "EPHALET TERWILLIGER".
Also known as: ELIPHATER TERWILLIGER EUPHATER TERWILLIGER ELIPHLETTE TERWILLIGER EPHALET TERWILLIGER ELIPHALET TERWILLIGER E.J. TERWILLIGER another possible variation: ELI J. TERWILLIGER
Anyways type "Cayuga" and "Sennett" in the search engine at this forum and you will find Terwilliger's (Twigs) that are closely connected. I cannot say to what degree they are related. They are closely related. Some may be "same name" Twigs and not part of your direct tree.