You can also have a mind that is easily distracted. It is similar to ADD but not the same. The injured brain can struggle to filter out background issues/stimulation. This can cause the mind to quickly get off on a tangent. One word in a conversation can redirect the mind or a visual stimuli can do the same. One can be in the middle of a conversation and see something across the room and start focusing on that and lose track of the conversation.

My neuro said it was different from ADD in how the brain processes thought.

Your description sure sounds like what I experience.

Was the sleep deprivation test an EEG with a sleep cycle that you had to stay awake all the night before ? Or is it in a sleep lab for a sleeping disorder ?