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I've got a pretty thorough knowledge of my GGG-grandfather's generation, born around the 1810s. 

I've now found a throwaway comment in a 1918 newspaper article from when his sister died: their "great-grandfather was 106 when he died" - no more detail given.

It would be great to find their great-grandfather, but I'd been struggling even to find their parents with confidence.  I know their names from a Scottish death certificate: surname BURNS, CLARK.  In the 19th century, this was essentially a Northumberland family, with some moves into Berwickshire/Roxburghshire as time went on.

Any tips on where to start, beyond the standard backward-parish-record-trawl - or even if this tidbit of information about him can help the search in some way? 

Can anyone help me find Robert Alcorn, please? (spelling very variable, I've seen: Aldcorn, Alcoran, Alcorne)

I've no reason to think he ever strayed far from Caldra near Fogo, Berwickshire.  He's described once as "of Sisterpath" (also near Fogo).  He was a "farm servant" or "steward" (presumably land steward).

He was not with his wife in the 1841 census and she's a widow on the 1851 census.  Therefore it's likely he died before 1841.
His youngest known child, Mary, was born around 1820 (age only from censuses) so unless there was an unknown alternative father, Robert died after that.

So looking at 1820-1841 (possibly later) for his death.  To give an idea of his age, his wife was born in 1780.  Their first known child, William, was born in 1807 so marriage shortly before that I guess.

All suggestions and/or tangential local knowledge gratefully received!

A wonderful 1901 newspaper obituary gives William Burns's birth as specifically as "the 30th April, 1811, at Kyloe, Northumberland, where his father was a shepherd".  His death cert shows parents as John Burns, Ann Clark.

He seems to have had siblings Thomas b1814, Jane b1816, Margaret b1826, and tentatively also Mary and Isabella.  Would anyone be able to find the birth/baptism record to hunt out siblings for me?  And going to earlier generations would be fantastic but they were shepherds and so may have moved around all over northern Northumberland and into Berwickshire.  Or just a list of BURNS entries would be great.

My first time asking for a lookup, so please correct my etiquette as you see fit!