Togusa doesn't have a clue. He is observant, but his instincts don't kick in well about a person until he's known them for a little bit. So, while he situates Daisuke (the pup won't run off far, his paw injury doesn't let him move too fast), he is slowly counting, to give Tatsuma a head start.

When he is off, he is trying to be stealthy about his own approach. He's just hunting down a teenager, after all. It wouldn't do for him to be caught too early. But where, oh where would he hide? He heads towards the tree line, vaguely in the direction of civilization.