Something to consider is that in general, there is no such thing as 'too much rest' to anyone. There are monks who sit and follow their breathing the whole day through, thinking as little as possible, and breaking only to eat, sleep, or use the bathroom— and some will follow this routine for months and months.

So in that way, it doesn't really matter how "little" you do, as long as you're not getting any more brain injuries.

Anywho, for me, the most important thing is to stay out of bed and to stay active for the whole day, even if "active" just means doodling or going for a slow walk for an hour, doing dishes, and so on. I would call those activities "restful", in that they don't make me feel anxious, dizzy, physically, or mentally overwhelmed. Of course, to someone in the first weeks and months following a TBI, these things might not be considered restful, and would probably cause a potentiation of symptoms. So I second Deuce's idea of "do what you feel is right," because likewise, what's rest to me may be stress to you, and vice versa.