I'm afraid your comments don't provide any examples which show that it was common to say that a daytime or a night time would be involved with an event when no part of a daytime or no part of a night time could be. Maybe you could start a new topic to discuss your findings.
It doesn't anwer the explicit question of the original post, but the reason why this question was raised.
The answer to the original question would be that no, a day is a day and a night is a night, and it is common to count them separately
Dt 10:10 And I have stood in the mountain, as the former days, [for] forty days and forty nights, and YHWH also listens to me at that time
Mt 4:2 ... After fasting forty days and forty nights, he was hungry.
Mt 12:40 for as Jonah was in the belly of the fish three days and three nights, so will the Son of Man be in the heart of the earth three days and three nights.
We find the nights mentioned and the days counted in
Lev 8:35 ... and you abide at the opening of the Tent of Meeting by day and by night [for] seven days
This rite is not mentioned later, it cannot be used as a proof or counter-proof to the thesis that it would have been only 4 days and 3 nights, but hardly anybody would understand it like that.
The creation myth of the Genesis mentions the evening before the morning, but the counting of the days is written after the morning:
Gen 1:5 ... and God calls the light “Day,” and the darkness He has called “Night”; and there is an evening, and there is a morning—first day.
Gen 1:8 ... And God calls the expanse “Heavens”; and there is an evening, and there is a morning—second day.
...
The date (ritually relevant for holydays and shabbat) starts at sunset
Ex 12:18: In the first month you are to eat bread made without yeast, from the evening of the fourteenth day until the evening of the twenty-first day.
In the Psalms, we usually find both, the day mentioned before the night and the evening mentioned first:
Psalm 55:10 Day and night they prowl about on its walls; malice and abuse are within it. Its walls are patrolled day and night against invaders, but the real danger is wickedness within
Psalm 19:2 Day after day they pour forth speech; night after night they reveal knowledge.
I never found a day and a night counted as two days, and would be illogical.
Psalm 77:16 The day is yours, and yours also the night; you established the sun and moon. Both day and night belong to you; you made the starlight and the sun.
Psalm 55:17 Evening, and morning, and noon, "" I meditate, and make a noise, and He hears my voice,
The first notion of a 24 hour day (with the night counted as a part of the day), and one of the rare Jewish documents that counts the evening as part of the preceding day is in the Book of Jubilees (late 2nd Temple period):
Jub 49:19 When the house of God is built in the land of their inheritance, they shall go there and sacrifice the Passover lamb in the evening, when the sun goes down, in the third part of the day.
All prescriptions for a day last at least from the morning until the evening, but the third day always begins in the morning.
Ex 19:10-11 Then the LORD said to Moses, “Go to the people and consecrate them today and tomorrow. They must wash their clothes and be prepared by the third day, for on the third day the LORD will come down on Mount Sinai in the sight of all the people.
For two days and the third day for resurrection, compare
Hosea 6:1-2 “Come, and we turn back to YHWH, "For He has torn, and He heals us, " He strikes, and He binds us up.
He revives us after two days, " In the third day He raises us up, " And we live before Him.
But I haven't seen any indication that two nights become three because of any kind of counting.
