Was cleaning out storage cabinets today,found 2 of these. I believe it attaches under the dashboard and is used to adjust the carburetor. ( for the ladies )
Didn't the model A come with a knob meant to adjust the carb already? Mine has one from the factory. Maybe it is for a T or other auto make. I have an automatic carb control for a Model T, but it is much different than the one you show.