Pikatok followed the same rotational path that Kei'taro did, except her path dislodged enough snow that a line was visible behind her. That was all well and good, as it meant one of two things.

Either Pikatok, the Guardian of the Southern Gate to the Spirit Realm, either intended to leave the sancutary of the circle she was creating, or she didn't. In the case of the latter, she would have certainly laid a trap - though Kei'taro had no idea what it might have been; after all, he couldn't see through snow. It also meant she would be confined to that area, if she intended to lure him out towards aforementioned trap. 

This was all well and good, as Kei'taro still had another few facets to layer unto his trap. So far, he had completed one portion of his plan, and was underway with the second. This time, he would play the game smart, instead of fast and loose. He continued his circle, making it look like he was looking for an opening in the woman's defenses. All the while, his Thunderbird tattoo was still glowing, reaching another level of strength. In another few seconds, he could enact the third part of his plan. 

His eyes darted to and fro, looking between Pikatok and the hole she was trudging - he decided to add another wrinkle. He would draw her plan into the open, and to do this, he continued circling. His movements were surefooted, though precarious, as he was atop snow- but he was ready for that. His circling motion would, if Pikatok continued her current course of action, allow him more time to see what type of trap she had laid for him, and whether or not she intended for him to walk right into it. 

Whatever his father wanted had better be good, if he was going through all this strategy to actually defeat Pikatok to get into the Realm, instead of waiting her out.