g.f.:
I can tell ya when it's complete, when ATC says so, that's when.
Proof:
Late night (1am), new pilot making first night landing with crosswinds, cleared ILS approach, in weather, at a field with a closed tower, so I didn't think about the coming complication. Break out below radio coversge, vacate the runway, do the "after landing", thank the pax, help get new plane put "to bed" with ground crew who are unfamiliar with new plane--lots of "stuff" happening. Wait, you know what's next....."Sir, the Fire Department called, ATC wants your flight plan closed."
So, the approach is over when ATC says so.
Wrong on two accounts:
1. The issue was failure to close (yes, close, not cancel) an IFR flight plan at an uncontrolled airport. ATC has to hold open the airspace in those circumstances. That makes them very unhappy after some time has passed.
2. ATC doesn't "say so" in these circumstances but they are working from the same book as the pilot, which places the burden on the pilot to close his IFR flight plan once landed at an uncontrolled airport. At a controlled airport the tower closes it for you.
In the air the pilot can elect to cancel IFR, weather permitting, which then closes the IFR flight plan. But, you can't cancel IFR once on the ground, only close the flight plan.