In the end, Kane failed to train himself in that aspect. Resting with his eyes open wasn't difficult, but keeping himself awake while he was relaxing was. He ended up falling asleep several times, and then a few seconds later, he would wake up feeling like he was about to cause his own death because of that.
Jacob woke up after sleeping for three hours; as expected, he didn't rest as much as he wanted, but he took Kane's place in watching over the area. At that point in time, Kane was so exhausted that he could barely think straight… the worries of being killed by those strangers while he slept were the last thing he could think of.