Well all - I do believe the case may be cracked! ;D
It took a lot of doing and a significant amount of frustration trying to search the Census but I have finally found the answers.
Although I am still struggling with the reasons for some of the things that happened.
The reason none of us could find Abraham PARKYN/PARKIN/PERKIN prior to the 1861 Census is because that was NOT HIS NAME at all!
With all else having failed I decided to search FamilySearch for anyone named Abraham born between about 1820 and 1840 with a father named Joshua.
Abraham son of Joshua and nancy
ARTHUR of Down Hill baptised 18th February 1833 at
St EvalJoshua Arthur married Nancy Hicks at St Eval 8th April 1805
There were eight children from this marriage with Abraham being the youngest. All were born/baptised at St Eval as follows:-
Samuel bp. 3rd April 1810
Isaac bp. 28th June 1812
John bp. 20th October 1814
Priscilla bp. 6th May 1817
Joshua bp. 18th March 1821
Dorothy bp. 31st August 1823
Jacob bp. 5th February 1826
Abraham bp. 18th February 1833
In 1851 John, age 37 born St Eval, was at Camborne with two daughters, Priscilla 14 and Mary J 12. His wife was not present but he was stated as being married. Also in the household was Joshua Arthur, lodger age 32. Joshua stated he was born at Camborne so I don't know what connection there may have been. John's brother Joshua was born at St Eval and would have been only 30.
In 1851 Samuel and wife Mary Ann were at St Ervan.
Returning to 1841:-
Joshua and Nancy had children Dorothy, Jacob and Abraham at home at Downhill, St Eval
By 1851 Joshua was widowed (Nancy was buried at St Eval 21st October 1847 age 62). He was still living at Downhill but Priscilla was now home with Dorothy and there were two Arthur grandchildren in the household.
And from here we get into the area where reasons seem to be lacking!
I should point out that it was not until the 1830s I think that I found the name Parkin (var.) in the St Eval baptism registers.
In 1841 son Joshua was working as an agricultural labourer over at St Ervan but he was then known as Joshua PARKYN, age 20.
In 1851 I finally found Abraham at Trewoolla, Crantock, employed as a farm servant. He was indexed as ABLOM ARTHUR!
We know that Abraham PARKYN married Eleanor Glasson at East Newlyn in 1853 and I now know that Parkyn was not his birthname.
And then in 1841 we have what is apparently brother Joshua also recorded as PARKYN.
But ..................
24th December 1838 St Eval by Banns
Isaac PARKYN, of full age, bachelor, labourer of St Eval, son of Joshua Parkyn, labourer married
Ann WILLIAMS, of full age, spinster of St Eval, daughter of John Williams, labourer
In 1851 at St Agnes we find Isaac Parkyn age 37, born St Eval, farm labourer. With him is wife Ann, age 44, born St Allen, and children Mary Jane 11, Ann Maria 9, Christianna 7 (all born St Eval) and Joshua 6 born Newlyn.
So WHY did three sons of Joshua and Nancy Arthur change there name to PARKYN?
CT