Sforno on Exodus 34:33
ויכל משה מדבר אתם אבל בעוד שהיה מדבר אתם היה בלי מסוה, כענין והיו עיניך רואות את מוריך וכאמרם ז''ל (פרק קמא דעירובין) ואי חזיתיה מקמיה, הוינא מחדד טפי
(English translation is from Sefaria. It includes editor's commentary, so it is not literal):
ויכל משה מדבר אתם
but while he was still speaking to them he did not wear the cloth. This corresponds to Isaiah 30,20 “your eyes should look at your teachers.” As our sages explained (Eyruvin 13, Rabbi Yehudah Hanassi speaking) “if I had looked at his (Rabbi Meir’s) teacher’s face instead of merely at his back I would have been even more learned.”)
So, it seems that Moses put on the veil while he was walking around the camp not teaching the people.
This puzzles me. The people asked Moses to put on the veil because they were afraid of him when they saw his face shining. Does this mean that only while he was teaching them, they weren't afraid any more, but afterwards, they were, again?