The BTS records for Aubourn show:
James and Elizabeth Ruxton (Jacob's nephew and niece and children of Robert Ruxton) were baptised in Aubourn in 1603/4 and 1605/6. Robert Ruxton married Isabell Goodwin in Aubourn on 24.5.1603/4. He appears to have had a previous wife (Joan/Joanne Read) buried in 1601/2, whom he married in Aubourn in 1593/4. Robert Ruxton was mentioned in Artemas's will. Isabel wife of Robert Ruxton was buried in Jan 1607/8 in Aubourn, her son Roger was baptised only a few days later, so she could have died in childbirth. Robert married Agnes Brown after this (Agnes died 1621/2). Little Elizabeth died in childhood in 1613/4 (buried 10.6). Robert Ruxton was buried on 20.8.1630. The Bassingham tithe book (exact date not clear, but 1614-65, see Lincs to the past) records a Robert Ruxton of Marlborough (Aubourn, where Artemas also lived).
Christopher Wright and Elizabeth Gresswell married in Aubourn on 10.2.1605/6 (=Jacob's sister Elizabeth Wright mentioned in his will).
William Gresswell, husbandman of Aubourn (possibly likely Jacob's step father) was buried in 1602/3, sadly only left an Admon, no will, but did leave an inventory worth around £86. Elizabeth Gresswell (most likely Jacob's mother) was buried at Aubourn on 15.3.1617/8 and I would love to find her will since she apparently left one!
William Gresswell (the brother) appears to have had a stillborn (abortive) child buried in Aubourn in 1608/9. He died at Bassingham in 1630 and left a will: LCC Wills 1630/370. The will mentions his wife Ann, James Ruxton of Marlborough (Aubourn, no relationship type mentioned), William Wright (his nephew), his mother Elizabeth Gresswell's will (which I have not yet found), Elizabeth Wright (again mentioned in relation to Elizabeth Gresswell's will), his nephew the brother of his nephew William Wright whom's Christian name he didn't know, the children of his cousin William Gresswell.
A John Browne had a child in Aubourn in 1599 (Marie). He also appears to have possibly been from Bassingham.
Anthony Hewing (or Herring) had children in Aubourn in 1595/6 (Thomas), 1597 (Jane), 1601 (Mary) and 1610 (John) and 1616 (?name as poorly legible), he was recorded as a labourer in 1610. A William Hewing was buried in Aubourn 11.7.1610/11. I have not yet seen his will, but it is listed as William Hering of Aubourn LCC Wills 1610/407 (listed under Herring). This may help clarify the family connection further? An Anthony Herring married a Mary Snell in Thorpe on the Hill on 1.5.1596.
As to the Goodwin surname (Isabel, Jacob's sister and Christopher his brother). There are 2 wills I haven't seen yet: Jas Goodwine of Awboron LCC Wills 1574/ii/54 and Jas Goodwine of Awbourn LCC Wills 1574/i/185 (likely to be the same person), these may help clarify who Isabel and Christopher Goodwin were or mention Artemas/Jacob?
These people therefore seem to have been closer in age (or younger) to Artemas than to a man born in around 1550, also if Jacob was born in 1550, then his son Artemas cannot have been born in 1563, meaning Jacob was either much older or there was more than one baptism for an Artemas Mackinder (which certainly didn't take place between Sept 1569-Sept 1570). I would therefore not be surprised if Jacob was Artemas's (and Roberts) brother and his mother Elizabeth later married William Gresswell, since this would explain why Jacob's sister Elizabeth Gresswell didn't marry until 1605/6 (whilst of childbearing age since she had at least 2 sons). Jacob's mother may even have had another husband before becoming a Gresswell, since we have the Goodwin's. The will of Jas Goodwin (1574 may therefore be of some real interest and once COVID restrictions improve I will look this one up!)