Fionnghal
I think the 15th Foot was in Dublin in 1800 - both 1st and 2nd Battalions. If you take a look at
http://youroldbooksand maps.co.uk/british-army-list-1800.html and at 'The British Army List 1800' and click on the right-hand screen shot it just happens to show the 15th Foot record. I believe these lists are available at Kew. You could, of course, buy it but I don't believe they show 'other ranks', only officers, and I guess if your man's later occupation was 'labourer' he wasn't an officer.
The main army barracks in Dublin was known simply as 'The Barracks' at the time (later the Royal Barracks and now the Collins Barracks).
I was lucky enough to find my ancestor's service documents at Kew, but of course he was in the army much later. I've looked on the catalogue for Thomas Jackson under WO97 but the only Jackson I could find for that period was a James Jackson (WO97/364/15 - if you put this in as a reference and 'Browse from here' you'll be able to confirm). Thomas would only be in this series if he received a pension anyway, which he would only have done had he been invalided out. Enlistment before 1806 was technically for life, so I'm not sure where that leaves you.
I don't think the Thos Jackson in the 2nd Foot Guards is your man - the 2nd Foot is a different regiment from the 15th Foot - the 2nd Battalion 15th Foot is what you're after - it's often written 2/15th in shorthand.
Perhaps you should try and come up good on the Lottery and pay a visit to TNA at Kew - I'm no expert but they have so much information down there that you may well turn up something. Anyway, good luck with your searches.
Paul