Sounds right Logbook.
I've measured a few of them. Do you have an antenna chamber biff44? Typically you rotate the antenna, measure phase, then slide it back or fwd and remeasure phase. Then note where your antenna is compared to the center of rotation. Wide beam antennas are tricky to make a good setup, since things bounce off the absorber around them, narrow beam antennas are easier.
If your antenna isn't a monopole or bicone, then your phase will start moving/shifting at wider angles, say 60 degrees off boresight or more.
You'll typically measure an H plane phase that's longer at wider angles, and an E plane phase that's shorter.
Picture an X band horn antenna, at boresight the energy radiates from say 5 inches inside the antenna. As you move in the Eplane, the radiation is from the front edge as the electrons turn the corner, and hence you have moved 5" closer or shorter. In the H plane, the radiation appears to be from the far side of the horn since it's a flat plate with plain view to the far angle (the near wall outer edge will also radiate a little, but much less than the far wall flat inner surface) you then measure slightly longer phase delay in the H plane at far angles.
Phase center is a sum of all the energy from the antenna. That data is then combined to a single point.
The phase center should be spec'd as a single point, with +/- phase error, over a range of angles.
Are you building a phased array? If it's an array, the elements near the one you're testing affect your phase center results.
kch