The entitlement to wear the RAF Flying Badge or 'wings' is covered in QR (J) 727. In order to retain wings it is necessary to have been designated as combat ready (CR) in role rather than just doing 6 months in role. It is very unusual to find a pilot who was CR on one type and who subsequently failed a fast-jet crossover to be re-roled as a navigator; they would normally either revert to type or re-train on another multi (or helo) or go to be a QFI.
I have however, flown with several navigators who were pilots but who failed to get CR and were re-roled as navigators. In this case their entitlement to wear pilot's wings ceased and so they could not just elect to wear pilot's wings if they felt like it.
I cannot explain why someone who went through an entire and successful career as a navigator would want to wear pilot's wings.