LORELAI: [hangs up, speaks to Sookie] Hey, Shields and Yarnell, what’s going on?
Shields and Yarnell, a famous mime duo formed in 1972, comprising Robert Shields (born 1951) and Lorene Yarnell (1944-2010). Their speciality was a sketch called “The Clinkers”, where they portrayed two robots. They had their own show, The Shields and Yarnell Show (1977-78), and appeared on hundreds of other programs, including The Tonight Show With Johnny Carson, The Sonny and Cher Show, and The Muppet Show. Career highlights included shows for two American Presidents, a command performance for Queen Elizabeth II, and a tour of China with comedian Bob Hope. They were married in 1972 and divorced in 1986, periodically reuniting to tour with their act.
Lorelai addresses Sookie as Shields and Yarnell because of the way she tries to get Lorelai’s attention on the phone.
In the picture, Yarnell is on the left and Shields on the right.
The Annotated Gilmore Girls 