As in some previous entries in this column, sometimes Disney Imagineers will tuck random props from old attractions and stick them where they fit in the new layout of somewhere else in the park. Assuming it's not plainfully obvious, most guests don't notice a prop from a long gone attraction adorning the wall of somewhere else in the park. In the AFI Showcase shop, which is located following the AFI Showcase portion of the Backlot Tour, there are a number of props in the store and on top of one display are some props from attractions that are very much long gone.
The director's chair indicates the name of a character from a film and it has a double meaning being here. Firstly, the character of Mumbles is one of the villains from the 1990 film "Dick Tracy", starring Warren Beaty. The film was a colossal failure at the box office, despite high hopes from Disney and an all-star cast. It had such high expectations that Disney went forward with plans for the film before it ever debuted in the theaters. This leads to the other reason why this chair is here and that's because it was a prop from the now extinct Dick Tracy starring in Diamond Double Cross attraction that ran from May 21, 1990 - February 21, 1991 in the old Theater of the Stars (the one that was where the entrance to Sunset Boulevard is currently).
Next to the chair is a clipboard that at first glance might be assumed to be also from the Dick Tracy film or attraction, but in fact it has nothing to do with Dick Tracy. However, it does have a connection to the Studios because it's a list of crew from the 1988 comedy "Big Business" that starred Bette Middler and Lily Tomlin. Still not seeing a connection to the Studios? Well, back when the Studios first opened, there used to be a restaurant where Playhouse Disney - Live on Stage! is currently called the Soundstage Restaurant. The restaurant was a counter-service restaurant that, for a time, was designed to look like a "live set" for the live-action film, "Big Business". You may not remember much of this edition as it was quickly re-done to look like a set from "Aladdin" and subsequently from "Beauty and the Beast". Clearly Imagineers had both the director's chair and the clipboard laying around and used them in the design of the AFI Showcase shop.