Began to trace it through

Maybe the confusion lies in the viscosity of the material through which one traces.
If I trace a pattern in nearly-set concrete, the tracing will be clearly visible, perhaps in perpetuity.
If I trace a pattern in water, the impression remains only for a few seconds.
If I trace a stick through air, in general there will be not be even a fleeting image, unless there is something in the air such as smoke.
But this is Harry Potter we're talking about, where sticks emit lightning bolts capable of killing, so it doesn't seem far fetched that a tracing wand might leave a little residual.