The cable is configured like this: --< (with the handle being on the left and the rear wheels on the right.)
A single cable from the handle pulls a metal bracket. The metal bracket holds two separate cables going to each rear wheel. If one cable brakes, it introduces enough slack into the system that the hand brake may become inoperative on both wheels.
It's more likely that the individual wheel cable has broken rather than the center pull piece simple because the center pull cable isn't exposed to the elements.
If the center pull cable broke, the hand brake handle would not pull on anything and the system would have no tension in it - lots of slack - when the handbrake is pulled.
If only a single rear brake cable broke, there should be a little resistance - only some slack - in the handbrake as the cable side that isn't broken would still operate.
As you've suggested, the only way to tell for sure is to inspect under the car. Some of the exhaust shielding will need to be removed.