Could it be that we have found a link?
Between you and Eileen, I feel that I'm/we're getting close.
I don't have the paternal name or place of birth for my John Drain, b. 1865/6, except for "County Antrim". My John also roomed with a John Drain upon a arriving in Chicago. My guess was that he was a close (perhaps 1st) cousin.
I've been focussing on "Henry" as a probable father's name, because my John's 1st-born son was named Henry, and that would seem to follow Irish patronymic tradition (especially conisdering I do know that the 2nd-born son was, indeed, named after John's wife's father).
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. My Drain trail has been cold for about a year now!