Eye issue; You should ideally look at the rut and at the approaching track.
Turn issue; I have a totally different approach to this though, the right wrist. I just took a gary semics class and I specifically asked him about dragging the brakes in a rut. Here is his answer and it works very well;
Front: This brake servs one purpose, to slow the momentum of the bike. You should NEVER use it is a rut. If you HAVE too, that means the bike is not leaned over far enough, lean it flatter. If the bike is going low, turn the throttle more(ie, go faster).
Rear:This brake controls the attitude of the bike and the front wheel position. Again, you should never use it when you are accelerating out of a rutted turn of any turn for that matter. Use it to guide the front wheel into the rut. Dragging the rear brake approaching a rut wil make the front wheel pull in and back and give it a better bite making the trip into the rut more accurate and fast. When turning, the BALL OF YOUR foot should be pressing on the outer peg. If you so this properly, there is no possible way for you to use the rear brake without moving you foot. If your rear brake is set up properly, while sitting you will not be able to brake and keep your foot on the peg at the same time.
I listen to these techniques as they come from a famous trainer, but it all really boils down to 2 things; The bike is not leaned over far enough, or tyou are going too slow for the lean of the bike. Using the brake in a turn to keep the bike put is indicative o anoter problem that must be fixed. Also, dragging the brakes while accelerating is a really good way to wear them out.
BTW, his(semic's) techniques are awesome. Sice returning, I have increased my speed alot and I can ride for HOURs straight without tiring, not to mention I no longer look like I have a goon riding style.