i've had to replace the GPS several times on my '10 Roadster. it would appear that the original GPS is a common weak point on the first few model year Roadsters.
Based on my research - in march 2013 triumph updated the gear position sensor for a lot of its models, included all* (tourer not mentioned) the rocket models (rocket iii, classic, touring, touring SE, touring (ABS) and roadster). this came into effect at engine # 596481.
did you ever have to change yours? what kind of mileage you have?
the map is a little different for when you are in N than when you are in gear - this may account for the rough running you've experienced while your N light is dancing, i don't know - my idle used to dance when N light was dancing.