Words did not persuade Jacob. But the wagons did.
"They told him all the words of Joseph which he had spoken to them. And when he saw the wagons which Joseph had sent to bring him, the Spirit of Prophecy which had gone up from him at the time that Joseph was sold, returning, rested upon Jacob their father" (Genesis 45:27). Targum Pseudo-Jonathan supplies the detail the Torah leaves implicit: ruach nevu'ah, the Spirit of Prophecy, returned.
The sages are unanimous. From the day Joseph was sold — the day Jacob saw the bloodied coat — the Ruach ha-Kodesh, the divine spirit of prophecy, departed from the patriarch. A father consumed with mourning cannot prophesy. Grief is a wall the Presence will not pass through.
Rashi, quoting the midrash, says the Shechinah rested on Jacob only in his joyful hours. For twenty-two years there was no joy, so there was no Spirit. The patriarch who had wrestled with the angel at the Yabbok (Genesis 32:25), who had dreamed of the ladder at Bethel (Genesis 28:12), had been spiritually silent for over two decades.
Now the wagons. The midrash reads agalot, wagons, as a coded message — reminding Jacob of the eglah arufah, the broken-necked calf, the Torah topic the two of them had been studying when Joseph disappeared. When Jacob sees the wagons, he remembers the lesson. When he remembers the lesson, he knows the message is really from his son. When he knows it is really from his son, joy returns. When joy returns, the Spirit returns.
The Targum stitches the whole chain together in one sentence. Prophecy left when love broke. Prophecy came back when love was restored. For the Jewish tradition, this is the basic architecture of the spirit: it follows joy, and joy follows reunion.