The Irvine (Ayrshire) Harbour Trust has a Harbour Book detailing the cargoes in and out of Irvine from 1821-1824. Under the code Gr1/18/16 there are just two entries for the ship 'Jean' [which I think may actually have been 'Jane'] whose captain's surname was McElhago.
In July 1822 her 'cargo in' from Drogeda was simply listed as 'Ballast'. She then left Irvine on 20 August 1822, also for Drogeda, her 'cargo out' being 'Coals'. Her tonnage was 106. The Rate Charged is listed as 3. I don't know whether this number is a code or whether it means £3.0.0.
I think the captain must have been James McElhago who would have been 31 years old at the time. He had been married to Jane Harvey in 1819 and by 1822 they had had their first daughter, Elizabeth. In his profession as seafarer and captain, James was following in the footsteps of his father Robert.
Interestingly the same ship (here called 'Jane) is referred to in the 'History, Directory & Gazeteer of the County Palatinate of Lancaster', by Edward Baines, Vol. 1, Liverpool 1824. Under Coasting Trades to and from Liverpool to Drogeda we have listed the 'Jane', captain James McElhago, though with no further information.