Moses wore a veil over his face after Sinai, because the shining of his skin frightened the people (Exodus 34:30). But there was one moment he always took it off. Targum Pseudo-Jonathan on Exodus 34:34 preserves the rhythm: when Mosheh went in before the Lord to speak with Him, he removed the veil from his countenance until he came forth.
The Targum's small detail carries a huge idea. Before God, no covering. Before Israel, a veil. The human intermediary dresses down only for the divine audience, and puts the covering back on for the public one.
The rabbis drew out two meanings. First, practical: you cannot mediate with a screen between yourself and the One you are mediating with. The prophet must meet God face-exposed, or the channel is blocked. Second, theological: Moses' face was itself a borrowed light, and that light had to be returned to its source each time the prophet came back into the tent. Removing the veil was not display — it was re-charging.
There is also a poignancy here. Moses lived in two modes after Sinai. Publicly he was muffled, dimmed, kept at a reverent distance by his own people. Privately, in the Tent of Meeting, he was fully himself — fully lit, fully near. The veil was the cost of prophecy exercised in public. The unveiling was the prophet's private life.
The takeaway: the truest self is the one that stands before God without covering. Everything else — the veil, the distance, the careful titration of light — is a concession to the world's capacity to bear what a prophet has seen.