The special name give to the rising of stars
just before sunrise is
heliacal rising.
Pre-modern people who rose before sunrise
were often very aware of
heliacal risings since
that is when they would first see
stars and
constellations
that they had last seen just west
of the Sun at
sunset.
In the absent time, the stars and
constellations
were lost in the daytime
glare of the Sun.
The length of the absent time is various and depends on vary variable observing
conditions.
However it takes the Sun about a
month to move 30° relative
to the fixed stars,
including notably the zodiac constellations,
and 30° relative to the Sun
may be about as close to the Sun
as you can see a star
at sunset and
sunrise with just casual observations.
So about 2months for the
absent time.