However, because of the precession of the equinoxes, the error with respect to the vernal equinox (which occurs, on average, 365.24237 days apart near the year 2000) is 1 day every 7,700 years. By any criterion, the Gregorian calendar is substantially more accurate than the 1 day in 128 years error of the Julian calendar (average year 365.25 days)." (Wikipedia)

365.25 - 365.24237 = 0.00763 and 128 * 0.00763 = 0.97664. A better measure than 128 years ought to be 1 / 0.00763 = 131 years.

Similarly. 365.2425 - 365.24237 = 0.00013 and 1 / 0.00013 = 7,692 years.

However, I have used the measure 26,000 years / 360 = ca 72 years for a precessional movement with 1 day. My idea was to transform 26,000 years for 360º (in a circle) to how many years a precession with 1º would be.

A year is approximately 365¼ days, not 360 days. 26,000 years / 365¼ = ca 71.2º = 26,000 / 365.2425. There is no difference in using the Gregorian compared to the Julian calendar.

Precession moves the star dome ahead in the year with 1 day in ca 71 years, because the Gregorian and Julian calendars are firmly connected to Sun by way of the vernal equinox. Therefore it would be strange - indeed quite unacceptable - if precession would change the date for vernal equinox.

On the other hand, if not Sun but the stars (together with Moon) were the primary time-givers, then the diurnal cycle would surely not be defined as a calendar day but as a calendar night:

1. Night; to get dark, to fall (of night): he-po, it is getting dark. Formerly used, with or without raá, in the meaning of a whole day: po tahi, one day; katahi te kauatu marima po, fifteen days; po tahi raá, first day of the week; po rua raá, po toru raá, second, third day, etc. 2. Alone or as po nui, used to express the idea of good luck, happiness. He-avai-atu au to'ou po, I wish you good luck (when taking leave of someone). Very common was this parting formula: aná po noho ki a koe! good luck to you! Po-á, morning; i te po-á, in the morning; i te po-era-á, very early in the morning. Po-ará, quickly, rapidly, swiftly: he-iri po-ará, go up quick; he-ta'o itau umu era po-ará, he cooked it quickly. Po-e-mahina, formerly used of sleep-walkers (haha a po). Vanaga.

1. Darkness, night, late; po haha, dark night, gloom. P Tu. po-tagotago, darkness. Mgv., Mq., Ta.: po, darkness, night. 2. Calendar day; po e rua, Tuesday; po o te tagata, life. P Pau., Mgv., Mq., Ta.: po, calendar day. Churchill.

Western astrology seems to have been blinded by Sun at spring equinox, ignoring how precession moves the constellations in the night:

"Sidereal and tropical are astronomical terms used to describe two different definitions of a 'year'. They are also used as terms for two systems of ecliptic coordinates used in astrology. Both divide the ecliptic into a number of 'signs' named after constellations, but while the sidereal system defines the signs based on the fixed stars, the tropical system defines it based on the position of vernal equinox (i.e., the intersection of the ecliptic with the celestial equator) ...

The tropical system was adopted during the Hellenistic period and remains prevalent in Western astrology. A sidereal system is used in Hindu astrology, and in some 20th century systems of Western astrology.

While classical tropical astrology is based on the orientation of the Earth relative to the Sun and planets of the solar system, sidereal astrology deals with the position of the Earth relative to both of these as well as the stars of the celestial sphere. The actual positions of certain fixed stars as well as their constellations is an additional consideration in the horoscope ..." (Wikipedia)

More observant cultures continued to use their eyes:

... Far away, the Mangaians of old (Austral Islands, Polynesia), who kept the precessional clock running instead of switching over to 'signs', claim that only at the evening of the solstitial days can spirits enter heaven, the inhabitants of the northern parts of the island at one solstice, the dwellers in the south at the other ...