I did one where you drink the oil slowly over 2 hours from about 7:30. Take 4 TBSPNS every 15 minutes and chase it with a swig of lemon juice until you've had your limit of oil. (I had 2 cups!).
Other people on this site seem to do emergency flushes sometimes with the same results so I don't think it really matters what time you do it. It's probably just easier to pass the time if you can sleep through it! Maybe also a digestive thing. They do say 2am is "liver time" so maybe that's connected.