I'm not really sure how you're supposed to negotiate a corner without looking... :roll: Which would lose you more points? Looking or hitting the poles?
When you back up a car, you look behind you. At the very least, you use a rear view mirror. It would be silly to expect you not to check where your horse's feet are going. The purpose of a trail class is to show how well your horse can negotiate obstacles out on the trail. No one in their right mind would back around a corner without watching that their horse's feet were on the trail, especially if that trail was on a hillside.
So my vote here is to check to see where you're going. Train yourself to use as little movement as possible and not to be doing a whole lot of twisting in the saddle to throw off the horse. In the photo you appear to be leaning forward and turning a bit, but that could just be camera angle.
Sit straight like you would in an equ class with shoulders square. Practice doing straight back ups first, without poles or anything. It's okay to look back over your shoulder or down toward the ground so long as you're not twisting in the saddle. Do one step at a time, stopping between each step to settle your horse and yourself. Taking your time will help improve your seat as well as the horse's head set.
By starting out without poles, you reduce the stress that both you and the horse may be feeling. Relaxation is the key to a smooth trail class. Once you can back ten steps or so without turning in the saddle and keeping your horse relaxed, set up some poles and practice. I always like to set them wider than you'd find in a class so that the horse feels confident to begin with; it also helps you determine if you're twisting and throwing him off without him actually hitting a pole. When you can get through a wide back up, narrow it up and perfect it again.
You can work on a pivot on the forehand without poles, too. Again, the less you have around your horse's feet to begin with, the smoother the results in the end. I always try to set both horse and rider up for success rather than failure; sometimes it takes a little longer to get where you're going, but it's well worth it in the end!