I am not sure if these will suffice as some are from scripture and only one is an outside source, the Babylonian Talmud.
In Genesis 42, Joseph commands his brothers to be placed in prison for 3 days, but before the third day ends he brings them out. (Part of the day counted as a day). From 1786-1570 BC
David stumbles upon an Amalekite slave that had been abandoned for 3 days and 3 nights but the slave said it was only 3 days. Don’t know if this would show if Hebrew time reckoning was applied to the slave’s comment or it shows that the Amalekites also used the same reckoning for time. Somewhere between 1048 BC and 1011 BC.
Rehoboam tells Israel to give him three days to determine an answer and he gives it on the third day, instead of waiting for the night of the 3 day. C 931 BC
I Kings 20 states the armies camped for 7 days, but it was on the 7th day that they started to fight. (Part of the day counted as a day). Somewhere between 874 - 853 BC
In Esther 4:16 She tells all the Jews to fast for 3 days and three nights. Afterward, she would go to the king. In Esther 5:1 She goes to the king after 3 days have passed. C 479 BC.
Rabbi Elezar ben Azariah wrote “A day and night are an Onah and the portion of an Onah is as the whole of it.” (Jerusalem Talmud:Shabbath ix.3 and Babylonian Talmud:Pesahim 4a). Mishna, C 200 AD and Talmud C. 500 AD.
You’re looking at a span of over 1500 years in which a part of a day was considered a whole day.