hehe, Gaelophone. A person that speaks Scottish Gaelic is a 'Gael' (although this is debated as 'gael' translates to 'highlander' - and there is ambiguity in that can mean someone with the Gaelic language, or a geographical 'Gael' (someone living in the Highlands of Scotland or a combination of both factors. But Gaelophone is more fun!
'Gael' generally refers to a member of the Goidelic-speaking peoples in general: Irish, Scotch, or Manx. Would 'gaeilgeoir' generally refer to Irish speakers specifically, or to speaker of Goidelic in general? What would be the Irish term to Goidelic-speakers in general? Or Celtic-speakers in general?
Perhaps it's just a question of style, but for me an Irish speaker is an Irish person who is speaking (whatever the language being spoken) and an Irish-speaker is a person speaking Irish, whatever country the speaker might be from. I believe Irish-speaker should at least be acceptable as an answer here, if not the preferred answer.
No, that's not the phrase he uses to describe himself. He is from the Dingle Gaeltacht and did not speak a word of English till he was in his late teens; I specified Munster because I know the dialect differs in some ways from the standardized register. He had always referred to the language alternately as "Gaelic" and "Irish" and readily accepts both, which is why I asked. He might have chosen a different word to explain it to his American anglophone granddaughter, but again, that's why I asked.