It may be the connections, or the wiring as well. Not to add to the list of variables, but it would be difficult to determine where the problem is on this particular configuration.

What would need to happen would be for the switchbox to seamlessly allow one signal while allowing nothing from the second signal. Perhaps a higher quality box may do the trick, but you might try different cables. Since it's an older set, 1.3 or lower would probably be recommended for this situation.