LOTS of O'Callaghans in Co. Cork and Kerry. 247 Cornelius's in Co. Cork, 283 in all Ireland in the database. Find a specific county, parish, townland, town, and/or parents' names. Some of this may be in his military service rcd.
The UK National Archives has military service rcds back to Oliver Cromwell's time. You can ask the Imperial War Museum staff to assist in this. They know who to talk to.