We know when everyone usually tweets, so why not reverse engineer it and find when they sleep using SleepingTime. There is only one box to fill in, and that is the person’s Twitter id. No authentication is required so protected tweet streams will not be possible. Humorously this could also show when someone works and are not allowed to tweet as well.
You are presented with a clock showing the red areas that they tend not to tweet and it must be their normal sleep window. I am not sure how useful all of this is, unless you are looking for them to respond immediately.