A few answerers to the question Significance of Methuselah's death year replied with the claim that Methuselah died seven days before the Flood began, thus leaving Noah and his family as the only remaining righteous people on Earth. (Most of these answers are deleted as they weren't sufficiently high-quality.) Furthermore, two of them also said that the 7 days between Methuselah's death and the Flood was for a period of mourning. At least one commenter said that they had heard of this tradition before, but did not know of any support for it, and a request for references did not get a response.
I've never heard of this tradition anywhere else other than these answers. Where and/or when did it originate? Specifically, the tradition that 1) Methuselah died 7 days before the Flood and that 2) the 7 days were for a period of mourning.