Near the end of a band, without crossing it
Gemini's opening decan runs from the ingress to ten degrees. A 29 May Sun stands between about seven and nine, so it is in the last third of that band in every year sampled but never quite reaches the next one.
That is worth saying plainly, because dates a little later in the month do straddle the line and this one does not. The whole century of noon positions fits inside a window of roughly a degree and a half, and the top of that window still leaves a degree of clearance before the boundary at ten.
So the useful summary for this date is three items long: Gemini, a degree between seven and nine, and the first face. Everything a page can honestly say from the date alone is contained in those three, and most pages stop after the first.
Why the window is so narrow
The Sun covers a little under a degree a day, and a calendar date returns to almost the same solar longitude each year because the leap day corrects the accumulated slippage. Three common years push the date forward by about eighteen hours of solar motion, and February the twenty ninth pulls it back by a day.
The result is a sawtooth rather than a drift. A 29 May birth in 1932 and one in 2032 land within a degree and a half of each other, which is why a birthday can be given a degree even before the year is known. Only the hour of birth moves it further, and across a full day that is less than a degree.
What the tradition puts on this band
The Chaldean order of faces, Mars, Sun, Venus, Mercury, Moon, Saturn, Jupiter counted from zero degrees of Aries, arrives at Jupiter for the first decan of Gemini. The triplicity scheme, which allots a sign's decans to signs of the same element in order, keeps this one with Gemini and so with Mercury.
Under Jupiter the band is read as Gemini turned outward, more interested in the broad case than the immediate detail. Under Mercury it is read as the sign undiluted. Both are interpretation, and both would change if the writer changed scheme, so the useful habit is to note which one is in use rather than to treat either as settled fact.
The placements the date cannot reach
A Moon on 29 May can be in one sign or two across the day, and over a run of years all twelve have occurred. The rising sign is set by the birth hour and the birth latitude, and it changes completely roughly every two hours, so the date rules out nothing at all there.
The widget above takes a year, a time and a place and returns the Sun's exact degree and minute, the decan, and the distance to the nearest sign boundary. On this date that distance is comfortable, and the closer call, if there is one, is with the decan line at ten degrees rather than with Cancer or Taurus.
If the birth hour is not known the calculation defaults to noon. For the Sun here that is safe, since the whole day stays in one sign and one face, but a Moon or an Ascendant taken from a noon default is a guess and should be labelled as one.
Questions people ask about this
Is 29 May Gemini in every year?
At noon, yes, in every year from 1930 to 2035. The Sun enters Gemini around 20 or 21 May and does not leave until around 20 or 21 June, so this date sits well inside the sign.
How close is the date to the next decan?
Close but not on it. The highest noon position in the sampled span is around nine degrees, and the second decan begins at ten, so the first decan holds in every year.
Who rules the first decan of Gemini?
Jupiter under the Chaldean sequence and Mercury under the triplicity scheme, since that face belongs to Gemini itself. The two schemes are not reconcilable and a source should say which it follows.
Does the hour of birth change the degree much?
By less than a degree across a whole day, because the Sun moves a little under a degree in twenty four hours. It is enough to matter for a tight aspect and not enough to change the sign.
What does the date fail to tell me?
The Moon sign, the rising sign, the house positions and every planet other than the Sun. Those need a birth time and a birthplace, and they are the parts of a chart that differ between people born the same day.
Is a late degree in a decan read differently?
Some traditions treat the closing degrees of a band as transitional in tone, but that is commentary rather than a rule. The technical position is simply that the Sun is still inside the first face of Gemini.