Got it. If it’s stationary to you, time-light isn’t a factor. If you’re rotating relative to it, aberration is but I’m still not convinced that’s a fixed value. It seems like it would have to go from zero at sunrise to some maximum value at noon, and then back to zero by sunset.
Otherwise incredibly bizarre things happen. Consider it. Pluto, though apparently in Sagittarius, would "actually" be far off in a different constellation altogether. Any star that is near an integer multiple of 1 light day distant would actually be near its apparent position. Any star near (n + 1/2) light day away would be 180 degrees away on the diurnal circle. So if you are looking at a galaxy near the celestial equator, half those stars would be "actually" in front of you, and the other half behind you somewhere, if this notion were true.
If you’re rotating relative to it, aberration is but I’m still not convinced that’s a fixed value.
Diurnal aberration (aberration due to the rotation of the earth) is an incredibly small effect (0.3 arcsec) that varies with latitude. The only way for the sun's real position to be 2.1 degrees in advance of its apparent position is if the sun is orbiting the earth at 11,000 km/s.