Rats!
In Taiwanese folklore, today, the third day of the new year, is the day when the rats hold their weddings, so we have to get to bed early to give them a free playing field.
The reason for this saying seems to be that during the first day of the new year, which is spent with the husband's family, and the second day of the year, spent with the wife's family, are filled with gambling, ie, mahjong, through the night. This seems to be pretty much the way things are, so by the the third day, it is time to lay off the gambling, so here's a reason to get to bed early.