So today i replaced some rear subframe mounts on my BMW E36/5 Compact, and it went well. But i wanted to replace the reverse light switch aswell, because the reverse lights didn't work, and the bulbs are fine. When i tried to loosen the screw on the switch it broke in two pieces, and the one half is stuck in the transmission now.. (Manual transmission - 1,6 liters). The switch is made in aluminium.
What do i do now? Do anybody have any tips or tricks to fix this? I'm in a rush, because the car is going to be inspected in 11 days..
My mechanical skills are allright, but I'm no pro

Thank you