He took his information from The Bards and Authors of Cleveland, which was written and published by George Markham Tweddell, the Stokesley printer, in 1872. The full title was The Bards and Authors of Cleveland and South Durham and the Vicinage. Tweddell has a short chapter on John Jackson
who for six-and-twenty years was master of Rudby School, was so much esteemed as a classical and mathematical teacher that the sons of the principal inhabitants of Stokesley used to travel daily to and from his academy to avail themselves of his instruction. Many of the sundials still existing in Cleveland are of his manufacture, that at Rudby Church being one.Tweddell quotes in full the lyrics of the song The Cleveland Fox Chase, for which John Jackson wrote both the words and the music. It begins
The glimpse of Aurora appears o'er the hills,The morning's inviting and fair;The murmuring streamlets and fine purling rills,Along with the sweet-scented air,Invite the gay sportsmen; and first do appearThe two noble chiefs of Greenhow,With famed Gis'brough's lord, and the hounds in the rear,In hopes to cry off - Tally-ho!
(The gentlemen mentioned were Sir William Foulis, Bt, his brother John Robinson Foulis, and William Chaloner, owner of the hounds).
John Jackson was evidently a man of many talents. The notice of his death in the Hull Packet of 21 June 1808 records
On Friday the 27th ult. that very useful member of society, Mr John Jackson, of Hutton Rudby school, aged 65. He was a universal scholar, and many years a contributor (in every department) to those learned and entertaining annual publications, the Ladies' and Gentlemen's Diaries.(I think the Diaries was an Almanac-style publication)
As for The Bards and Authors of Cleveland, which covers authors and poets from Caedmon to Francis Mewburn, the solicitor for the Stockton & Darlington Railway, you can read it here, as archive.org now has the text online. A full account of its contents is to be found here on the website dedicated to the life and works of George Markham Tweddell (1823-1903).