LM, could you please separate the issues of safety and legality in your posts?
I trust that the flying lessons are in a public transport aircraft. By attaching a camera to the aircraft without a CAA or EASA minor mod invalidates the C of A. And no, it can not be classed as baggage. I am surprised that your instructors are allowing you to this sort of dangerous activity.
If you install a light camera with a suction cup or clamp, do you seriously think that's illegal? And where is the line then? If I install my handheld GPS with a clamp on the yoke or with a suction cup on the window, is that illegal too? Or if I put my checklist on the panel with a clip of some kind? Do you have a reference for this?
Look forward to watching the video of you or your instructor being bashed over the head by a tripod & camera, I am sure that it will get many laughs on Youtube.
Great attitude. Particularly since safety/security was not discussed at all up to you posting that comment.
Personally, I think everybody has the common sense so make sure that the suction cup is big enough to hold the camera in question, even under vibration or g-loads. And then you'd still use a tie-wrap or something else to make a secondary attachment to somewhere.