NavList:

​Hmm. Correct me if I am wrong, but my understanding is that the purpose of a world-wide geodetic survey during the 1970s (particularly during the 1970s, but probably started before and certainly continued after) ​was to determine a map showing, for any point on the earth's surface, to what extent a gravitationally determined zenith axis (that is, an axis normal to a horizontal plane determined by a sensitive bubble level) did not pass through the centre of a spherical earth. 

A geoid was then created which effectively adjusted the latitude and longitude of every point on the surface of the earth such that, to first order, these deviations of local gravity were corrected for. That geoid is WGS84. 

If the latitudes and longitudes according to WGS84 are used for a given place on the earth, you should find that a vertical axis normal to the local gravitationally determined horizontal plane will pass through the centre of the geoid. If you then use a very accurate theodolite to observe a star passing through or close to your zenith, it should be where you expect it to be. The result is that any parallax in altitude should not have any accompanying parallax in azimuth.

However, the WGS84 geoid is just an approximation, so there will still be small second order corrections that need to be applied to the local zenith axis such that it passes through the centre of the WGS84 geoid.

In conclusion, it would probably be more accurate to say that to second order, the parallaxes of Right Ascension and Declination are the vector components of the parallax of altitude.

Geoffrey Kolbe