Yes, you’re right, a capacitive sensor might also work.
The good thing is that all your suggestions gave me several potential solutions. I’ll start from mine (proximity sensors), and move to other ones if this one is not good enough.
For the time gap, as it will be launched by people using this box, they are anyway limited physically to a certain speed. And i guess this speed is lower higher than what the arduino can process. But this will be part of the test 
See you soon, for more concrete news