Nobody will question your COR if you have an Irish passport and indicate Ireland as your COR.
Thank you for the reply but Ireland *isn’t* my country of residence. Or are you saying that as a workaround I should just say it is ..
Ireland is your country of citizenship (active passport) and that is what you use for Crossing borders. When you travel with a Global Pass you would need a formal current form of ID to show your COR, and no inspector would dispute you presenting your Irish passport if you claim Ireland as your COR. Remember that would limit you to a max of 2 days travel in the whole of the island of Ireland ( a strange quirk of rail networks).
If you declare the UK as your COR you would be limited to the same max of 2 days travel, but now n the UK. You would then need to carry a form of proof as a resident of the UK.
I’m resident in the UK and have travelled 4 times using a global pass with my Irish passport. Have never been asked for a UK passport. I think you’ll be fine using your Irish passport. Ticket inspectors only look at your pass.
I’ll just add that I have never been asked for a document proving UK residence.