Unfinished and uncertain)):
Since I am astrographer, I wanted to understand these two planes rotation, since in galactic plane are most deepsky objects and ecliptic plane (zodiacal signs) are essential for positioning.
My guess isthink that really since north ecliptic is l=97 degrees (LacertaLacerta), b=+30 degrees, from earth with 23,5° earth axis5°axis tilt it will appear to be Cassiopeia 120° (hence 23,5° offset, which goes statically in this direction - away from center galaxy (celestial sphere is pointing just "only" 3° lower(than ecliptic) toward galaxy disk, b = 27°) it will appear to be Cassiopeia 120°. For stargazing it has more sense consider Celestial sphere be pointing to Cassiopeia (or 27° above (toward galactic north pole) Cassiopeia).
YouIf you are in mid-EU latitude (50°), you may use something like Stellarium and check positions of these planes in solstices and equinoxes (as I did) and it may help you to get feeling for their orbits. Some pictures bellow also may help you to visualize it:. If you are on further away lat., you will see it differently, but principle will be same.
False followingFollowing toward CassiopeiaCassiopeia (in 60° tilt down) on Celestial sphere: If you on the equator watch 60° up to north (to compensate solar system downward angle) at vernal equinox day moment, when sun is at highest point, which is now in Pieces constellation (RA – 0h), than you would see Cassiopeia (you can check it in Stellarium when sun light is turned off). At this time/ place 23,5° Earth axis does not offset you on equator, but as you have been going up, you went up 23,5° off (hence Lacerta - 97°).