Danny, recalling our previous conjectures about HF aerial configurations on various VVs, is it possible that your excrescence is the fairing for a trailing aerial? I know nothing about Targets or their towing, but that tube looks a little on the flimsy side for such use don't you think?
A pity the serial number is not apparent, for it would at least confirm your ID. The (duck egg blue?) band around the rear fuselage isn't apparent in the Auster pic, suggesting more than one VV in Italy at least. As Franek says, most likely use was TT (for the Spits also at Grottaglie?) . If so it was presumably available on a request basis to fighter units in the area (to keep their hand in?). I wonder if there was a local TT Flight for it and its sisters to come from? Presumably it didn't do any dive bombing, for surely we would have heard of that! Nice pic though. Fred Lax was obviously fascinated by it and other one off visitors to Grottaglie, which is fascinating in its own right, given its airship hangars.