ChuckC, I've wondered the same thing myself.
When I went through rifle training in the Marines, we were taught to focus on the front sight, so that the target and the rear sight were out of focus. They could even tell if we were focusing on the target instead of our front sight, as our shots would circle around the bull rather than grouping inside. They called it "chasing the bull" (and called us something impolite, as I recall).
I wonder why it's the opposite when gap shooting a bow? I suppose you could try it both ways and see which way works the best, but there is probably some explanation for it.