Nothing much, i'm afraid. I’m blundering around in a dark bricked up tunnel!

I’ve tried A2A at
<http://www.a2a.org.uk/search/index.asp> but, although there are a few records referring to the 15th, nothing about a Thomas Jackson.
i found his marriage lines .. funny spelling and all

Extract of an entry in an OLD PAROCHIAL REGISTER
Parish of Aberdeen, County of Aberdeen. Register of Proclamations of Banns and Marriages
“1798 Sept 10th Thos Jackson and Elspet Ingram
Upon the 10th day of September One Thousand Seven Hundred and Ninty Eight By the Revd Mr Wiliam Blake Minister of St James Chapel in Aberdeen were lawfully Married in the said Chapel after due proclamation of Banns Thomas Jackson Soldier in the 15th Regt of Foot and Elspet Ingram in Aberdeen Daughter of the Deceast William Ingram late labourer in the parish of Bellie. In presence of these Witnesses Patrick Wead Soldier in said Regiment and Elizabeth Ray Residenter in Aberdeen"
Her records were easily enough found.
Someone kindly sent me the main movements of the 15th, and they do seem to have been in Ireland c.1800-1802 but exactly where is the question. In the end, it may not be important because even if Irish records had existed there in some parish record, they’d probably have perished with almost all the rest in 1922.
We haven’t even worked out if he was Aberdonian or, a Yorkshire man

who ended up in Aberdeen with the 15th - which was a Yorkshire regiment.
Regimental Rolls can apparently be viewed on request at the PRO, but i just get lost going round in ever-decreasing circles on that site.
What i have observed however, is that the name Jackson was commoner in Yorkshire and Lancs than other parts of England and very uncommon in Scotland, although the name has had a small presence in Aberdeen for some 100s of years. That was just an interesting observation; it didn’t help me find him. If he was of a soldier family, he might have been born anywhere.

Interestingly, we find an earlier Thomas Jackson marrying in Aberdeen and he too, was a member of a Yorkshire regiment. He could just be our Thomas’s father but that is a long shot and improvable to date. We’ve found no children for him, which isn’t surprising as he probably had each one in a different country, depending on where he was serving!
This earlier couple are:
“in Aberdeen, 12th Nov. 1753, Thos. Jackson, soldier in Capt Master's co. & Beauclerke's Regiment and Janet Snowie.”
i found an Aberdeen burial:
Thomas Jackson, abode – O Abd; 83yo labourer; PR O/M; bur 22 Jan 1835
This is the ONLY Thos J. burial i could find in Aberdeen but that doesn’t mean there weren’t others.
If he's ours, he'd have been b.c.1852 which could be right for the earlier couple plus,
Our Thomas Jackson is recorded, on his other 2 daughter’s bapt lines, as being a labourer [which matches this death] – he’s obviously out of the army and settled/resettled in Aberdeen. That ties in with finding that the 15th had disbanded in 1802
This date of death also ties in with him not making it to the 1841 census.
so that lot does look a mite hopeful

if unprovable

but. none of which has helped us track down his birth, or his daughter Catherine’s, and they’re the critical forebears

I’m just 200yrs too late enquiring

thanks for asking, Ticker

le durachd
fionnghal