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It was reported in at least 85 newspapers. Some say that the father was "said to belong to Northumberland". One says they worked at Clydebank and were on a visit home. Their address is sometimes given as New Prestwick. The ages vary. Most say Annpit Quarry, a couple say Bell Rock Quarry.

The quarry in the link below is in the area of Annpit Road today and is probably the place.

https://maps.nls.uk/geo/explore/#zoom=18&lat=55.48159&lon=-4.61820&layers=168&b=5

However, if you go to the north and west of this quarry, you come to two others near the sea. You will notice the Bell Rock is marked nearby them.

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From a quick look at the censuses and the ScotlandsPeople indexes:

Robert Kilgour's marriage to Christian Forbes is recorded in Aberdeen on 25-4-1801.

Looking at Kilgour deaths with mother's maiden name Forbes we get:

Jane Kilgour d Nigg, Kincardineshire 1872, aged 70
Alexander Kilgour (the surgeon) d Nigg, Kincardineshire 1874, aged 70
Harriet Anne Kilgour, d Old Machar, Aberdeen, 1881, aged 61
There was also a sister, Christian (see 1861 below)

Jane and Harriet did not marry. In 1851 Jane is described as a gentlewoman supported by her brother. Harriet, who is living with her is described as a gentlewoman. Also present is a nephew, Patrick Kilgour, aged 17, a student.

In 1861, Jane and Harriet, both described as annuitants, are living with a nephew, George Carr, who is a doctor. He was born in 1835 to Robert Carr and Christian Kilgour.

In 1871, Jane Kilgour is living at Green Arbour Cottage, Nigg, and is described as an annuitant. With her is a niece transcribed as Margaret "Corn", but it should probably be "Carr".

From the Dundee Courier 21-2-1874:

At Loirston House, Aberdeen, on the
19th inst., Alexander Kilgour, M.D.

Loirston is in the parish of Nigg, just south of Aberdeen.

In 1911, FindMyPast transcribes it as Sydney Harrold Luffman.

Looking at the original document, Harrold does have a double r. The writer's S and L are similar, but not exactly the same. They begin L with a stroke from the top and S with one from the bottom. Capital L appears later on in "Labourer". The writer has written Luff[]ma, missing out the final n. The bit in [] is not an o, but seems to just be an extra part of the m. Quite possibly the writer has written Luffnma, putting the last three letters in the wrong order.

Below is a link to the entry in the (riding) Horse Tax Roll dated 14th July 1794 showing "James Brounlee of Headlesscross" paying tax on one horse.

https://scotlandsplaces.gov.uk/digital-volumes/historical-tax-rolls/horse-tax-rolls-1785-1798/horse-tax-volume-27/39

Below is a link to the Horse Tax Roll for 1797 showing "James Brounlie Headlesscross" paying tax on one horse.

https://scotlandsplaces.gov.uk/digital-volumes/historical-tax-rolls/horse-tax-rolls-1785-1798/horse-tax-volume-30/15