I know that we should be constantly in watch but does anyone know what time of day is most critical?

I have heard that 'twilight' is important and this is just after 5am in Jerusalem. I am based in UK and that would be just past 3am my time however for the last several days I am being woken at just past 2am consistently and last night with a greater sense of urgency. It's always at 2.10am precisely - Anyone able to shed any light on the likely time?