My daughter had a sleep deprived EEG when she was 5 at Cook's. Her EEG was scheduled for 2 p.m. and we were told to keep her awake for 12 hours prior. My husband woke her up at 2 a.m. and then he kept her awake by playing computer games with her all night long and then we kept her active up until the EEG. The idea is for the child to relax and fall asleep during the EEG. She fell asleep instantly--as soon as the technician turned off the lights and left the room. The staff was amazing and yes, they do understand that childen who are sleep deprived can be extremely fussy. If I recall, we had the results within a couple of days.
Overall, it's a very easy process. However, I imagine there is a big difference going through the process with a 5 year old vs. a 1 year old. At least I could explain "why" to my daughter.