I have no evidence for a Manx link. The reason for looking was that the only mariner who fitted the criteria in 1861 was the John Cain in Peel. I have looked closely at all the Elizabeth Cain's born in the short period in 1838 and found just seven in the BMD (including a Kain). Several of those died in infancy. The few that survived did not have a father called John who was linked to the sea (three were well inland in places like Birmingham and Notts). Isle of Man having no BMD at that time means I can't eliminate the Elizabeth Cain I found in Peel.

I suppose another possibility is that Elizabeth wasn't registered. It is believed that 10% of births weren't registered in the early days of civil registration.

I found Mary the huckster - thanks. Interesting! Another possibility.