So, the mention of the third month reinforces the time context of Pentecost.
So, there was a time of sanctification, and then God appeared on the third day and thundered the Ten Commandments.
Tradition suggests that Pentecost was when God gave the law. However, there is a difficulty to be aware of. As we just read, it was on the second day of sanctification that the whole nation washed their clothes. It was National Laundry Day. But if the third day was Pentecost, then Laundry Day would have been on the Sabbath, which is not something God would have commanded. Washing clothes is work for a preparation day.
However, if we move the starting point back one day and put Laundry Day on the preparation day, then the law would have been given on the Sabbath. But not just any Sabbath; the 7th Sabbath, the final day of the perfect perfection of time.
