How ... if at all ... should those who follow the Old Rite liturgically celebrate S Patrick?
The LMS ORDO, the obvious guide for those who use the 1962 Missal or Breviary, envisages S Patrick having only a Commemoration at Lauds and Low Masses today (I am talking about England, Wales, and Scotland).
I think it is clear that this is wrong ... at least, for those who in celebrating the Old Rite accept the evolutions in local calendars which occurred under Roman direction up to the imposition of the Pauline Rite and the de facto disappearance of the old calendars.
In the 1940s, the English, Welsh, and Scottish dioceses had differed greatly, some hardly noticing S Patrick, while a dozen or so classed him as a Greater Double just like S Gregory on the 12th. In the changes which came in with the 1960s, one would expect the 'Grd' to convert into a '2 Class'. And I have a 1969 ORDO, from the very eve of the disappearance of the old Calendars, in which S Patrick is a '2 cl' in the whole of Great Britain (1cl in Ireland, Commemoration "outside the British Isles").
I floated this question three years ago, and the erudite Rubricarius ... how could he fail to ... provided the answer. You will find it in his comment attached to this post. I remain grateful to him for this elucidation; and for a very great deal of liturgical information over the years.
The conclusion, which is I think beyond doubt, is that S Patrick should be observed as a Class II feast in England, Wales, and Scotland. Vespers, according to the 1962 conventions, will this year 2018 be of the Sunday following without any commemoration.
(In the older 1940s Calendars, there seems no rhyme or reason about which British dioceses noticed S Patrick: Liverpool, for example, despite its Irish diaspora, failed to do so! Incidentally, "All dioceses in Scotland" used a rather attractive Mass Egredere [cf Genesis 12:1-2]. And, before the 1950s, the Gospel of the Lenten Feria did duty as the Last Gospel. What a very edifying custom that was.)