Deuteronomy 16:1, seems to show that the Israelites departed on the night of the 15th. Since we know they were in the homes during the Passover, and were told not to leave their homes until the morning, it seems like they kept Passover on the 14th.
Follow this:
(CLV) Ex 12:6
And it will become a charge of yours until the fourteenth day of this month. Then they will slay it, every assembly of the congregation of the sons of Israel, between the evening hours.
There is night; then there is day; then there is night again. The day is between the nights.
The lamb is slain on the 14th during the day, between the evening of the 14th, and the evening of the 15th.
(CLV) Ex 12:7
And they will take some of the blood and put it on the two jambs and on the lintel, on the houses in which they are eating it.
They haven't eaten it yet, and they are preparing for the night when the death angel will come. By placing the blood on their doorposts, they are entering a threshold covenant with YHWH. They have invited him into their homes as a member of their family. They just sacrificed the god of Egypt to do it. They have repented and put away false gods. They have just left spiritual Egypt.
(CLV) Ex 12:8
Then they will eat the flesh on this night, roasted with fire, and with
unleavened bread; over bitter herbs shall they eat it.
They are eating the Passover on the first day of unleavened. unleavend bread is to be eaten for 7 days starting on the night of the 15th.
(CLV) Ex 12:22
Then you will take a bunch of hyssop, and you will dip it in the blood which is in the basin, and you will touch the lintel and the two jambs with the blood which is in the basin. As for you, not one of you shall go forth from the portal of his house until the morning.
Again they entered covenant when they put the blood of the lamb on their doorposts on the 15th, the first day of unleavened, they may not leave their houses until morning.
The death angel passed over on the night of the 15th. They left the land of Egypt on the morning of the 15th.
(CLV) Ex 12:11
And as thus shall you eat it, with your waist girded, your sandals ion your feet and your stave in your hand. You will eat it in urgent haste. It is the passover to Yahweh.
Why? Because they will be leaving quickly in the morning. When the sun comes up the Egyptians will know who was killing their gods, because YHWH told them to mark their houses with the blood of the Egyptians' false gods. After Yashar El killed off Egypt's false gods; YHWH killed of all of Egypt's firstborn, Yes, YHWH tested Yashar El's faithfulness to him right out of the gate. He made them put their light on a lamp stand, for all the Goyim to see.
Yashar El left spiritual Egypt in the darkness of the 15th, they left the Goyim of Egypt by the light of the 1st day of unleavened.
(CLV) Ex 12:12
For I will pass through the land of Egypt in
this night and smite every firstborn in the land of Egypt, from human even unto beast, and on all the elohim of Egypt I shall execute judgments; I am Yahweh.
Which night? The night of the 15th.
(CLV) Ex 12:13
Then the blood will become a sign for you on the houses where you are. When I see the blood I will pass over on you. And there shall not come to be a stroke on you to cause ruin when I smite in the land of Egypt.
(CLV) Ex 12:14
Hence this day will become for you a memorial, and you will celebrate it as a festival to Yahweh. Throughout your generations shall you celebrate it as an eonian statute.
What day is this? What are they remembering? How will they remember it? The next verse gives us a great clue.
(CLV) Ex 12:15
Seven days shall you eat unleavened bread. Yea, on the first day you shall eradicate yeast from your houses; for anyone eating what is leavened, from the first day unto the seventh day, that soul will be cut off from Israel.