I've found Stephen's baptism
On 6 March 1836 at St Mary's, Elland, son of Sarah H
olstead, spinster.
In 1841 he's living with his mother, her husband (William Hill), her parents and siblings, and another child John Holstead (aged 3, also baptised at Elland as son of Sarah, spinster), at Elland with Greetland.
In 1851 Stephen is with his mother, stepfather and brother (in Elland with Greetland), and in 1861 he's with his mother and stepfather - but listed as Stephen Hill, son.
Still no sign of Stephen after his marriage, and a few other puzzles... another son Joe, presumably a twin to Walter, born and died MarQ 1865, not baptised with Walter so maybe died very soon after birth.
William Hill Halstead, born DecQ 1870, with his mother in 1881 but not found afterwards. But there is a death of a William Henry Halstead in Halifax, in the JunQ 1881 which could be him
. I guess the 'Hill' could be a reference to Stephen's step-father
Another twist is that on his marriage (20 Oct 1888, St Matthew's Rastrick) John Richard Wood, Betty's son before she married Stephen, lists Stephen Halstead Wood, woollen engineer, as his father, though this has been crossed out. Wondering whether John said Stephen Halstead when asked but the vicar added Wood as that was John's surname.... If Stephen was his father though, it ties in with the 1911 entry for Betty, 6 children born, 3 have died.
So if the children (born 1862 to 1870) are all Stephen's, then maybe he did go to America at that stage, which would explain why he's not on the 1871, 1881, 1891 or 1901 censuses, and it is only in 1911 that Betty has the opportunity to say where he is (and he's described as deceased on Joseph Edgar's marriage on 31 Aug 1912 at Rastrick).