There is nothing to do to use it, just start the app... I would have expected it to always say NEAR actually in your case, since your screen doesn't ever turn on on a call automatically. Now my app does say 0.0cm or 9.0cm, not near and far, using Proximity Sensor Finder. I think it is Phone Tester that gives the Near/Far responses.
Also, go into a very dark room with the lights off, then start Proximity sensor finder... can you see a faint red light just at the tip of the shortend of the Verizon "checkmark" symbol indicating the sensor is functioning?