The second Irish reference occurs in a 1659 'All Ireland Census', which was taken during the 'reign' of the Commonwealth Protector, Richard Cromwell. It includes the Gaelic name MacGiolla Chairge which at least one author (MacLysaght) thinks is the Gaelic version of McIlhagga, though as I've made clear elsewhere, not the one to be preferred.
Third, and most significant because we clearly have here the Anglicised use of our name which has come down to us, as in Ayrshire there were three references to the Hearth Tax, so there are also three to the Hearth Money Rolls for a Townland called Cogry in the parish of Doagh Grange, in Antrym Barony in the present County of Antrim in 1669. The three clan members referred to are Alex McIlhago, Allexander McIlhago and James McIlhaga (our first 'a' ending). All three living in the same small place would imply that they all belong to one family. Two Alexanders may well mean a father and a son, and hence one of them brother to James. What we would hope for, of course, is a clear link back to a West of Scotland family. At present our fairly extensive knowledge of the clan in 17th Century Ayrshire has no Alexanders at all and only two Jameses. One James is too late to be considered (James son of David McElhagow born Kirkmichael 1674) and the other is extremely unlikely. He was James, Son of Thomas McIllhaggow, born 1653 in Kirkmichael. Admittedly there are no further references in Scotland to this James and we do not know what happened to him. He could have gone to Ulster but by the time the Hearth Money Roll in Cogry was compiled he would only have been 16 years old and we need to ask whether he would have had time to establish himself and to own a property with a fireplace on which he was charged tax. It is, I regret to say, somewhat unlikely.