As talks between the European Union and the U.K. on the terms of Brexit enter a critical phase, two of the main participants—the leaders of Ireland and Britain—are in very different form. One knows where he is going; the other still can’t be sure.

In March, U.K. Prime Minister Theresa May agreed that the withdrawal deal would include a backstop option requiring Northern Ireland, though part of Britain, to remain in full alignment with EU customs and single-market rules unless and until an alternative way was found of ensuring...