I'll use Desmond for my question.

When he traveled in to the past. His body in the prestent looked like he was asleep or he was staring out in to space.

What about his body in the past?
I know left from and came to in the phone booth, but the man was in boot camp. It was only a small miricale that an officer didn't find him in the phone booth.

So my question is. When he was bouncing back and forth, fine. I guess his body would be okay. What about the times when he doesn't do that for days on end.
Now that he has his contant. He is more stable for a lack of a better word.
Where is his body in the past? Does it have to be in a safe place? Is it even there?

First off he nevered traveled anywhere, his 1996 consciouness was pulled forward through time to 2004, and he is no longer jumping, it was an isolated incident that was resolved by finding his constant, if he didn't he would have died in that episode.