The vertical deflection occurs in the first few precession cycles after the bullet enters into a crosswind and is forced to realign it's axis with the oncoming air-flow. In other words, as the bullet is torqued to weather-vane into the wind, it sets up a gyroscopic action which results in the bullet being deflected down when it's axis is torqued by a left-to-right crosswind and vise versa. (this applies for a right twist barrel. As Michael stated above, the effect is opposite for a left twist barrel, which is very rare).
The vertical deflection is a close to a fixed angular deflection, meaning that if there's .25" of vertical deflection at 100 yards, it grows to about 2.5" at 1000.
Here's where it gets tricky (and where I think Vaughn's explanation is incomplete and misleading).
Since the vertical deflection is angular, but the horizontal deflection is not, the angle of deflection on the target face is greater at short range than at long range. For example, if there's 0.5" of horizontal deflection at 100 yards, accompanied by 0.25" of vertical, that's a deflection angle of ~27 degrees. At 1000 yards, the horizontal wind deflection will have grown to much more than 5", probably more like 100" while the vertical deflection has only grown to 2.5". This now only makes an angle of less than 2 degrees. The reason for this is because the wind continues to act in the horizontal plane, but the vertical deflection, once established near the muzzle doesn't continue to compound as the bullet goes downrange.
Bullets launched with higher stability factors will have a greater component of vertical deflection than bullets launched with lower stability factors.
There are practical considerations.
Most places that you're likely to shoot long range have some kind of terrain, meaning the land isn't perfectly flat. If you have a strong enough wind to cause a large horizontal deflection, the chances are good that the terrain will actually generate vertical winds which will deflect the bullet vertically and mask the above effect.
On rare occasions shooting on very flat ranges, I've used knowledge of this effect to save some points in big wind changes. If the wind picks up strong from the right and I have to crank on a lot of right wind, I may go a click or two down to keep the bullet from striking high and vise versa. If you try to play this game when shooting over terrain which generates actual vertical wind then there's another variable to consider and it's usually more significant than the effect we're discussing.
I've thought about working it into a ballistics program. Part of the problem is that in order to calculate the amount of deflection you need to know obscure things about the bullet like it's axial and transverse moments of inertia, and some aerodynamic coefficients that the shooter will not know. Any practical solution would have to rely on a metric like the stability factor to approximate the deflection. Even if it could be calculated perfectly, it goes hand-in-hand with a wind call which we all know are not exact and may be overwhelmed by a vertical wind current.