After Lorelai explains to Rachel that Luke has been doing handyman chores around the house for her, she walks past the Town Troubadour, who starts to sing this song, but is interrupted by the whistling rival troubadour from across the street.
Sadness Soot is from Grant Lee Phillips 2001 album Mobilize, earlier mentioned. The song seems to be giving advice to Rachel, as it talks about embracing solitude without feeling sad, and being able to move on. It fits in with her final decision regarding Luke. Could it also be telling Lorelai not to be afraid to be alone, and that she doesn’t need Max?
The Annotated Gilmore Girls 