Thanks to GR2's posting I have managed to find a bit more. I see in the National Archives for Scotland that:
"Instrument of cognition and sasine in favour of Andrew Dunbar of Leuchold, as heir of deceased John Dunbar of Leuchold, furrier, burgess of Edinburgh, his father, in a tenement on the north side of the High Street, at the foot of Ireland's Close. Registered fifth protocol book of George Home, 22 April 1718."
Now I have then found online a volume called "NOTES ON THE NAMES OF THE CLOSES AND WYNDS OF OLD EDINBURGH" in which there is a section on Dunbar's Close which reads:
"Dunbar's Close [Edgar. Ainslie. Kirkwood]. Ireland's Close. Baile Brown's Close. Penston's Close.
The name is guessingly derived by Chambers [7] from Cromwell's victory at Dunbar in 1650, the error arising probably from the fact that some of his Ironsides lodged in the Rose and Thistle Inn there. [8] It is really derived from Andrew Dunbar of Leuchold, who owned a tenement in the close, from the flat lead roof of which [9] Cromwell is said to have watched the Firth of Forth, and his fleet there. [7]
The father of Andrew Dunbar was named George, a glover by trade, and his son George was 3rd bailie in 1737. [10] John Dunbar, glover, and his spouse acquired the property from John Penstoun, merchant. [11]
Notes
[7] Chambers, i. 178.
[8] Wilson, ii. 6.
[9] Prot. J. W. 3, 17/1/1753
[10] Prot. W. F. 6, 9/1/1754
[11] Prot. J. W. 3, 17/1/1753"
In the same volume the entry for Ireland's Close says: "Ireland's, now Dunbar's Close. There was a tenement of land on the north side of the Landmercat, on the west side of Ireland's Close, bounded by the tenement of the heirs of John Dunbar on the north."
Now I sense an error in the above in that I rather suspect that Andrew was son of John (as in the National Archgives reference), rather than of George, although George does seem to fit well as the son if it is then he who married Helen Fleming in 1733, as in my earlier postings.
I would not rely on the IGI, but it does contain some suggestive matches in Andrew Dunbar, son of John, married to Margaret Gilchrist in 1706 in Edinburgh and then they had a son called George in 1707, which would fit.
Returning to Forfarian's suggestion that I try looking at Scotland's People, I have paid my £7 and looked at a record for Dunbar of Leuchold which says:
"December 17 1697
George oldest e.s. to the Laird of Leuchold, baptised in his owne house (being in time of great storms) by Mr. Miller Minister of Kirkliston; Witnesses, The Laird of Dundass (the childs grandfather, Jo: Stewart of Newhalles (?)" [that last word "Newhalles" is unclear, so I may have it wrong and likewise the initials e.s. at the beginning (which might be p.s.)]
Sadly the above does not tell us the name of the father in this case. The above George might be the one that I seek (who married Helen Fleming in 1733), but that would mean the IGI find mentioned above (with George batpised 1707) would then become a red herring.
Now according to the IGI Andrew Dunbar married Elizabeth Dundas in Edinburgh 21/8/1688 and they probably had the following children
Margaret baptised 12/2/1693 at Dalmeny
Elizabeth baptised in 9/2/1700 at Dalmeny
John baptised 27/1/1704 at Dalmeny
Barbara baptised 10/10/1705 at Dalmeny
Andrew baptised 30/4/1711 at Dalmeny
Dalmeny is one mile from Leuchold, which is highly promising.
I can find no match in the pedigree of Dundas of Dundas for an Elizabeth marrying to a Dunbar.
HOWEVER the extract from Scotland's People is transcribed from a manuscript copy and it is unclear if the grandfather is Dundas or Stewart - anyone care to comment on this, please?
The IGI lists a George Dunbar baptised at Dalmeny 17/12/1697 with a father called Dunbar and a mother called Stewart, but no christian names given.
So to come back to GR2's earlier question, it does rather look as if Andrew was son and heir of John and that George was son and heir of Andrew. George appears to have had a son called John, but may also have had sons called Andrew and George (see my ealier posting), all of which sons' names are consistent with the family relationships that appear to be emerging.
I wonder if this new information suggests anything to you, please?
It is clear that a visit to Scotland to research more on the spot would be of benefit, but I struggle to do so and hence am seeking wisdom via the wonders of the Internet.
Many thanks,
Caspar