Just my bad wording... Sorry.
I'll try to be more clear with pictures.
1 2
........ .........
...s.... .........
...s.... ...s.....
...S.... ...sS....
######## #########
Let's assume that Beethro is to the southwest from this serpent. When the serpent is moving horisontally, it wants to move to left, and when it's moving vertically, it tries to move down.
Now, let's suppose that it's time for vertical movement in position #1. The serpent wants to move down to get closer to Beethro, but the tile is blocked by a wall. So it checks the tile to N (blocked by itself), tile to E (clear), and moves to the position #2.
In #2, it doesn't matter if it's vertical or horisontal phase - The serpent will move north anyway. Tiles at S and W are both blocked, so it'll start again checking N-E-S-W. (Doing those little circles you were wondering about)
Is there still something that's not clear?