I agree the angle is closer to RIR but from the clearest button pic I think the ribbon appears to have three parts, and the harp strings appear not to be cut off diagonally by a wing. That's more consistent with Royal Irish I think. I also wouldnt expect the RIR to have a shoulder title ending in 'Irish' or light chevrons.To me, the width of the harp on the button appears to be too great for Royal Irish Regt. E2A: now that you've mentioned it, I can believe there's an 'S' on the shoulder title, so quite plausibly as you've said, 'RISH'.
Once he gets it out the frame we'll probably discover we're all miles off and it's the Gibraltar Regiment, but still.