Seeking Timothy Callaghan from Cork

Hi all,
I would like to please ask for someone to have a look into an Irish ancestor of mine, Timothy Callaghan (b. c.1786). He came over to London some time in the 1810s, possibly as a retired Chelsea Pensioner. There is a Chelsea Pensioners' record that lists him as serving for five years in the 103rd Regiment and being born in the parish of St Ann's in Cork, but I'm not entirely confident that the document is him, though it's the best I have. St Ann's in Cork is a CoI church, but I'm not sure whether  'born in the parish' means that he was justy born in the area or baptised in the CoI (seems unlikely with a surname like Callaghan). He married Englishwoman Elizabeth Ginman in 1819 in Piccadilly, with one of the witnesses being a 'Michael Callaghan', presumably a brother or cousin of his. He probably died some time in the 1850s, being listed in the 1851 Census as living in London and an 'appraiser', being sometimes also listed as a 'broker' or a 'taylor', and an 'upholsterer' in the army record. He currently stands as a brick wall, and I would love to try and find a baptism record or any indication of his parentage and origins.
Thanks,
Francis