Whenever I don't get enough sleep I can feel it through out the day. My response time is a bit off, and my thought process just isn't as focused. I don't normally go out of my way to get into a state of sleep deprivation, but I recognize that it is an altered state of consciousness, albeit one that is less than pleasant to experience. The feeling of fogginess is a state that can be worked with in a magical context. Sleep deprivation causes a blurring, not quite in control feeling. That feeling is useful for doing magical work where you are raising magic through activity, such as exercise or ecstatic dance. The reason its useful is because you're pushing your current state of sleep deprivation through activity to a point of exhaustion which in turn creates an altered state of no-mind, which can then be used to focus on the goal the person wants to achieve.
Ideally what will happen is that a person will use a state of sleep deprivation in tandem with an activity such as dance. S/he will either create a sigil or will develop some other magical technique that s/he will employ while dancing. For the sake of example, we'll just say the person will focus on the sigil while dancing. Eventually when the person is truly exhausted, s/he will stop dancing, but will continue to focus on the sigil, using the exhaustion as a way to focus every last bit of awareness on it. Then when the person can't keep awake any further s/he will go to sleep, continuing as best as possible to focus on the sigil, so that s/he can charge it in his/her sleep.
When a person has been sleep deprived and goes to sleep exhausted the sleep can be much, much deeper, so this is useful because as the person sleeps s/he allows the sigil to germinate.
Now if the person has thought ahead, s/he will have the sigil positioned in such a way that when s/he awakes, s/he will see the sigil, and recall the activities of the other night, and in that process, fire the sigil. It's a long build-up, but its effective, because you combine a variety of states of awareness into the working and when it fires, all of that effort contributes to the realization of the possibility you want to bring into reality.