Brad,
You're exactly right regarding function.
There is a cable attached to the back of the handle. The cable travels through the firewall, and held in place with a firewall mounted bracket. It then travels down and through another bracket attached to the top of the transmission crossmember. It finally attaches to a lever on the back of the brake drum. There are a number of places the cable can bind, but most likely, the inner cable is rusted solid to the outer cable cover. You may be able to clean and free up your original. If not, replacements are available.
Tim