I'm shelving two sources I found for now. Neither provides images of original documents. Nevertheless, here's what they show:
Name: Wiliam Wilcockson
State: CT
County: Fairfield County
Township: Stratford
Year: 1655
* [Apparently, William may well have been alive in 1655. He did not have a son he named William. Of his sons, two non MP sons – John and Joseph – show sons named William: b. 1661 and b. 1671. Samuel's son Sgt. William Wilcoxson was born 1671.]
Page: NPN
Database: CT 1635-1807 Misc. Records
https://www.ancestry.com/discoveryui-content/view/2321479:3537?ssrc...
Name: William Wilcoxson
Gender: Male
Birth Place: EN
Birth Year: 1601 [This is the birth year for William Wilcoxson]
Spouse Name: Margaret Birdseye [From where Birdseye comes into this record as Margaret's pre-marriage surname, who knows.]
Marriage State: of MA
https://www.ancestry.com/discoveryui-content/view/1324447:7836?tid=...