I would try to get as directly in front of him as possible while keeping trees (including the one he's rubbing) between his eyes and me. Then I'd ninja as close as possible while he is distracted by the rubbing. When he stopped rubbing, I'd freeze. When he turned, I'd like to be shooting.
An elk's (and other deer) eyeball is shaped such that when his head is down, he actually sees farther; the focal point/lens alignment changes. That is believed to be an evolutionary benefit for spotting predators while their head is down eating. I've mostly seen whitetails, that are nervous because they think they have seen a predator, lower their head, feign eating, and when I move, they jerk their head up because they were watching me with that increased visual clarity. Their vision is also best to the side, so a direct frontal approach is at the periphery of each eye. They'll still see movement, just not as clear.
Does it matter that I would have just pee'd myself from the excitement of shooting that pig?