If it's a locution - and I suspect it is - it's not widely used, I never heard it or saw it until now. So I add myself to the club of interpreters that so many members count in this dictionary, and I comment that I believe has some relation to the early morning. It seems a scrackized way of alluding, with an exaggerated style, to the hours "after which it is customary to give the mass of rooster or mass on average", which is done at midnight; here ignoring the Christmas date, I guess. See also not knowing someone from the Mass the average.
