Just wanted to let you know which solution worked best. I tried metal parts that close an electrical circuit which worked only in 2 of 3 cases. For capacitive sensing the parts i wanted to detect were probably just too small, so that did hardly work at all.
In the end I opted for optical detection with an IR emitter and phototransistor pair (tcrt5000), as Grumpy_Mike had suggested. I had to use 2 per slot to avoid blind spots and the wiring is then with 26 phototransistors relatively complicated but the reliabilty convinced me. It works 100%.
As a bonus I even can detect when an "organ" is moved and I plan on using that information to trigger flash lights, electro shocks and a sirene as soon as the tweezers are in a slot. It's supposed to be quite difficult in the end.
I want to thank everybody in here for their help! Greatly appreciate it!