I think your question is more about the circuit required. To take a single switchable channel as an example you'd need: three RCA/phono sockets and a switch.
Assuming the box provided screening and the phono socket was secured to the metal of the box via the (negative) body of the socket you could simply solder unscreened wire to the centre connector of the (incoming) phono socket and then via the switch to the two (outgoing) sockets -- the switch providing the alternate paths.
For such a project I would start with a multimeter and a couple of different switches which wil help you work out what switching you require -- and to trouble shoot the finished assembly.