Man, I would fuck with my teachers for this one. Here are some ideas:

• Turn it off and on randomly, pretend you don't know what's wrong. If the teacher keeps pointing it out, say sorry but it's an older cam.

• Eventually just leave it off partway through a lesson. Say it broke and you can't do anything about it now.

• Get some colored glass. Say you fixed it, but the whole picture is now red. Or just get strong sunglasses and it's very dark in your room.

• Mix yourself a drink in full view of the camera. Say it's for after the lesson.

• Record a loop of yourself sitting attentively and typing and play it back instead of having a live feed.

The last one is probably the one you want to do long-term. The rest is just some fun for yourself.