The bungee was probably used as a vang - it holds the sail out / down when sailing downwind in light air. Typically it would be rigged from the vang attachment (the fitting just aft of the gooseneck, called a "tang") to one of the front corners of the boat. You attach it to the gooseneck to store it when it's not being used.

Here's a photo from Bob Curry's Tuning Guide:


Do a Google search for "Hobie 14 Tuning Guide" - the photos are the fifth item down.