WARNING: No GPS data. Check wiring." The wiring seems to be correct. Do I have a misplaced jumper?
Looks that way.
Possibility 1 - Tx/Rx mixed up. Tx from the arduino POV is Rx from the unit's POV.
Possibility 2 - Obvious question: you have tx/rx pins, ok, but does the GPS have power? Blinkenlights? Even if it has its own battery, you will want to connect ground. If it's on a shield, then that's a non-issue.
It's also suspicious that the comment says that the sketch assumes the presence of a 400-baud serial GPS device, but the software serial object is set to 38400. Oh - I see you have changed the pins. So you have modified the test sketch. Just because the arduino talks to your computer at 38400, doen't mean it's going to be talking to the GPS at that rate.
Google? Tell me about the RoyalTek REB-4216 GPS module.
Google: Here it is!
Hmm, ok. Page 7 indicates that it runs at 4800, 9600, and 38400. So ok, 38400 is belivable. Maybe try the other speeds?