What is trap focus (and why it's not possible on the D800)?

I have no D800 and hence do not know if this camera will do trap focus.

In any event, to try I think you need to go to the AF single servo mode with focus priority in custom menu a2 set to focus (shutter will not release until object at selected point is in focus, pp 281,282 of your manual if in English). Acquire focus on an object at same distance as your target area, recompose with (empty) target area at selected focus point, depress shutter. Theoretically when subject enters the target area which is at the focus point (ie focus acquired), the shutter will release.

If you are in AF-continuous servo you need to have the focus controlled by AF-On only, acquire focus, then release the AF-On button so it functions as if in AF-S.

Good luck

D4, D700, bunch of lenses.