Hi,
My coaching experience was primarily in American trap, with a side of American skeet. In both disciplines, "wood to wood" as we liked to call it, was an important issue. Just like your student, some of mine wanted to "take a look" to see how well they broke the target, which turned into a situation where, sooner or later, the shooter lifts his/her head from the stock BEFORE pulling the trigger, with a miss being the inevitable result. And yes, in line with Buster's duct tape suggestion, there were jokes about using super glue that went around!
Dry firing is often suggested in many of the shooting disciplines, and for the rifle/pistol shooter, is a much easier practice than for the shotgunner. But imagination's a powerful tool if harnessed correctly. In American trap, unless one's shooting doubles, only one round is allowed in the gun at any time. However, in International trap, the shooter is allowed two shots at the same target. Many of those shooters have been trained to break the target with the first shot, then use the second shot to break the largest surviving piece. This forces the shooter to keep "wood to wood" until the second shot's fired.
I used a "mental modification" of this practice with some of my students, having them break their target with the live round, then "follow" the biggest piece and imagine they're going to shoot it as well. They could even say "bang" on that piece if it helped. Many of them adapted to this kind of follow through and their habit of lifting their heads was easier to break.
Not being a rifle/pistol coach, I'm not sure how to suggest it to your student, but some adaptation, where the shooter fires on the target then has to stay down on the gun for an imaginery "second shot" may be something you can work out? If not, just plain ol' dry firing might help, too...
Good luck!
Rick C