01:01, mirror hour
Just past midnight, the clock reads 01:01, the one appearing twice, once for the hour, once for the minutes. A double mirror hour that shows up in the quietest part of the night, when the screen is the only lit thing in the room.
Two ones make two, the digit that only works in company. There is none at this hour, and that is the useful part: nothing on a screen at one in the morning needs replying to tonight. Two is a waiting number, not a stalled one. Whatever wants an answer will still want one at a reasonable hour.