I come up with a design that could work out for the logic game, it solves both splits output into multiple and false connections (e.g. connect an output to another output).

The idea is to have a directional wire that can only go from an output to an input and the output side is stackable, so you can direct it into multiple inputs.

Here is my design:

 

Connector diagram

 

I hope this is helpful for the project.