Where does the minhag come from when moving a Sefer Torah from one place to another to cover it with a Tallis?
Answer:
I do not know of this minhag.
There is a custom to cover a Sefer Torah with a tallis when it is not being used, for instance during yizkor, the reason being that leaving the Sefer Torah exposed while doing others things can be considered disrespectful to the Torah.
Best wishes.
