In fact,the dawn/evening ambiguity exists also for the common word for evening in Sanskrit: sandhyA. That comes from a word which means to join (sam- together dhi to establish). There were three joins in a twenty four hour period: when the morning met afternoon (midday), when afternoon met night (evening), and when night met morning (dawn). The word is today used almost exclusively (except in the phrase tri-sandhyA three joins) for evening.
In English, twilight has a similar ambiguous connotation, though it is used more often for the evening than for dawn.