He is in the records of the Royal Hospital Chelsea as b.1833, Ballinakill, Clifden, Galway, enlisted 88th Foot aged 18 in 1851, examined or admitted at Royal Hospital, 7th Oct., 1856.
There are at least two Gannons in the Crimea rolls of the 88th Foot. He may have served with brothers or other relations.
A general search shows other Gannons born in the same village of Ballinakill at about the right time to be siblings, one a John Gannon in the 49th Foot.
These may or may not be the man, but one looks to be a Patrick though his number is not given.