How much is the birth time is important in astrology prediction, if difference in birth time will have any significant difference in prediction. How much amount of difference can be insignificant for the purpose of astrology prediction.
Time is the most important to decide the lagan. You are born close to the Cusp meaning the Ascendant degree is at 29 degree plus, which means that within few minutes the ascendant will change. A change of lagan would totally change the Birth chart and predictions.