Hi gang.....good to be here!
More info on Elijahs origins has come to light via a nice lady doing some lookups for me in Huntingdonshire.
Descendants of William PERKINS
1 William PERKINS
.. +Dinah
. 2 William PERKINS b: Abt. 25 December 1719 in St Mary's. HUNTINGDON. Eng.
..... +Elizabeth ?
..... 3 Elizabeth PERKINS b: in St Mary's. HUNTINGDON. Eng.
..... 3 William PERKINS b: in St Mary's. HUNTINGDON. Eng. d: Abt. 13 April 1816 in Godmanchester. HUNTINGDON. Eng.
......... +Susannah BRAND b: Abt. 17 May 1741 in Godmanchester. HUNTINGDON. Eng. m: 21 February 1771 in Godmanchester. HUNTINGDON. Eng.
..... *2nd Wife of William PERKINS:
......... +Mary GARNER m: 12 January 1775 in Godmanchester. HUNTINGDON. Eng.
..... 3 Mary PERKINS b: in St Mary's. HUNTINGDON. Eng.
..... 3 Susanna PERKINS b: in St Mary's. HUNTINGDON. Eng.
. 2 James PERKINS b: Abt. 24 October 1721 in St Mary's. HUNTINGDON. Eng.
. 2 Dinah PERKINS b: Abt. July 1723 in St Mary's. HUNTINGDON. Eng.
..... +Thomas TAYLOR

m: 18 February 1759 in Old St. Finsbury. LONDON. Eng.
. 2 Ann PERKINS b: Abt. 10 February 1724 in St Mary's. HUNTINGDON. Eng.
. 2 Elizabeth PERKINS b: Abt. 5 June 1726 in St Mary's. HUNTINGDON. Eng.
..... +Edward RICHARDSON m: 12 March 1750 in HUNTINGDON. Eng.
. 2 John PERKINS b: Abt. 16 January 1727 in St Mary's. HUNTINGDON. Eng.
. 2 Daniel PERKINS b: Abt. 27 December 1728 in St Mary's. HUNTINGDON. Eng.
. 2 Frances PERKINS b: Abt. 27 December 1728 in St Mary's. HUNTINGDON. Eng. d: 1 April 1810 in Godmanchester. HUNTINGDON. Eng.
..... +John RIGNALL b: 1729 m: 27 November 1753 in HUNTINGDON. Eng. d: 31 March 1810 in Godmanchester. HUNTINGDON. Eng.
..... 3 John RIGNALL b: Abt. 7 September 1755 in Godmanchester. HUNTINGDON. Eng.
..... 3 Frances RIGNALL b: Abt. 13 October 1756 in Godmanchester. HUNTINGDON. Eng.
..... 3 Robert RIGNALL b: Abt. 2 February 1758 in Godmanchester. HUNTINGDON. Eng.
..... 3 Thomas RIGNALL b: Abt. 24 September 1759 in Godmanchester. HUNTINGDON. Eng.
..... 3 William RIGNALL b: Abt. 22 October 1760 in Godmanchester. HUNTINGDON. Eng.
..... 3 Philip RIGNALL b: Abt. 18 April 1762 in Godmanchester. HUNTINGDON. Eng.
..... 3 Alice RIGNALL b: Abt. 1 July 1764 in Godmanchester. HUNTINGDON. Eng.
..... 3 Elijah RIGNALL b: Abt. 7 December 1766 in Godmanchester. HUNTINGDON. Eng.
..... 3 James RIGNALL b: Abt. 13 December 1767 in Godmanchester. HUNTINGDON. Eng.
..... 3 Alice RIGNALL b: Abt. 6 December 1769 in Godmanchester. HUNTINGDON. Eng.
. 2 Elijah PERKINS b: Abt. 11 July 1732 in St Mary's.HUNTINGDON. Eng. d: Abt. 28 August 1787 in St. NEOTS. CAMBRIDGESHIRE. Eng.
..... +Ann DAY m: 14 April 1757 in HUNTINGDON. Eng.
..... 3 John Bingley Esq. PERKINS b: Abt. 18 October 1758 in St. NEOTS. CAMBRIDGESHIRE. Eng. d: in of Southwark. LONDON. Eng.
......... +Susannah CARELESS b: Abt. 17 March 1762 in EYNESBURY. CAMBRIDGESHIRE. Eng. m: 3 September 1782 in HUNTINGDON. Eng. d: Abt. 22 September 1790 in St. NEOTS. CAMBRIDGESHIRE. Eng.
..... *2nd Wife of John Bingley Esq. PERKINS:
......... +Elizabeth ? m: Aft. 1790
. 2 Phillip PERKINS b: Abt. 23 May 1735 in St Mary's. HUNTINGDON. Eng.
..... +Mary ODAMS

m: 11 July 1779 in COMBERTON. CAMBRIDGESHIRE. Eng.
..... 3 Elizabeth PERKINS b: Abt. 2 January 1780 in COMBERTON. CAMBRIDGESHIRE. Eng.
..... 3 Hannah PERKINS b: Abt. 30 May 1784 in COMBERTON. CAMBRIDGESHIRE. Eng.
. 2 Michael PERKINS b: Abt. 27 October 1736 in St Mary's. HUNTINGDON. Eng.
The question marks mean just that....a possible connection, however the direct line back from Bingley Perkins is certain.
They were a family of Millwrights, Elijah's settlement papers to St Neots in 1758, & William his brother settlement papers to Godmanchester in 1765., both from St Mary's.
We couldn't find William & Dinah's marriage....still more work to do.
I don't think John Perkins born 1812 is son of Eliza & Susanna's brother, their brother was born in 1794, & would be too young if he survived at all.
But there are plenty more Johns in this extended family from which he could be descended.
Cheers.
Milton.