Drill bits should be easy enough... I had a hand drill I used for pinning small scale models that would work, and probably at that scale, magnets would be better than a spring and pin. One magnet for the pin, (cylinder) and a disc magnet for the spring at the opposite polarity.
Given that the rest is plastic, there's no issues with the pin sticking to the maze.
I have a bench mounted dremel, but the drill I need is something like a .015
I love the idea of the magnet but to try and put it together would be almost impossible. I’ve experimented with a tiny bit of sponge however the recall is rubbish.