Suggestion: The 90 degree rotation of the horn radiation entities will materialize.

I'm not sure I understand your question, however the pattern and polarization from any horn antenna (or wageguide for that matter) with one probe will be in direction of the probe.  So if the probe is horizontal the horn will radiate a horizontal E field.  The patterns remain the same as when the probe is vertical, except everything rotates 90°.  If the horn is on a table and facing the ceiling the patern again gets rotated and the E field is parrallel to the probe and the H field is orthogonal to the E field.

Polorisation for the main and side lobes will be identical for the H-plane and identical for the E-Plane, no matter which way the horn is pinted.

Bottom line, for testing polorization either V or Horz placed won't make much difference because the polorarity of the horn must match the pol of the  source satellite or Boresite feed. It must be manually adjusted (unless you have a pol motor.)

Main lobe and side lobe depends on the source as well, typically for earth stations the side lobe should be about 14dB down from the main lobe, with each side being a mirror image of the other.

Also, Signals are not true Horz or Vert. Although they are not specified as eliptical, every linear signal has a small eliptical shape, which is where the slight horizontal component fits in.

Iden