This may work,
You have your board with each of the places the pieces need to go marked on it. Now cut a hole in each of the places. The hole needs to be the same shape and have the same orientation as the place for the piece. Glue the cut out to the piece.
Now when you try to fit a piece on to the board it con only fit in the right place and the right way round.
Fit a switch under the hole in the board when the piece fits it makes the switch etc...
Mark