It's a big arsed battlefield.
They would need an Army LITERALLY to patrol it all night long.
there are so many ways to actually enter the park that it would be virtually impossible to close them all without having thousands upon thousands standing shoulder to shoulder to do it.
Actually airborne assets (even a tethered balloon would do) with night optics could do the patrolling, with a quick reaction force to respond to intrusions would probably work. Wouldn't be 100%, but if a proper example is made of those caught, the problem would likely be much diminished after that.