Swivel connectors are not only unecessary, but advised against. To put it bluntly, they're a pain in the neck once they get a little worn.
Here's how the routing goes: The backup second stage is routed like the primary second stage is normally routed on a basic open water rig. The hose is a bit shorter, though, at just 22"... And there's a piece of bungee or surgical tubing that's attached to the mouthpiece of the second stage underneath of the zip-tie that holds the mouthpiece on. That way, the bungee is worn like a necklace, and is always situated "right there" so you can simply pick it up and swing it upright into your mouth. Skilled divers can even train themselves to do this without using their hands... They simply reach down with their mouth and grab the reg off their chest. This gives them the ability to switch to a backup without using their hands, which can be especailly useful if your hands are already full with lift bags, lights, or paniked buddies.

Of course, the "necklace" part must be kept short to accomplish this, and is the reason for bungee or surgical tubing rather than a non-stretchy material like cave line or string.
The primary second stage has either a 5 foot, 6 foot, or 7 foot hose on it. If it's a 5-footer, the hose is simply routed off of the first stage (like "normal"), under the right armpit of the diver, across the chest and up and around the left, backside of the neck of the diver... Coming around and ending in the mouth of the diver from the right side, just like a standard basic open water rig... Except that the hose makes a much smaller, more streamlined "loop" over the diver's right shoulder. To donate, a diver simply hands his buddy his regulator, which pops over the back of the diver's head and allows a full five feet of hose to be utilized. Despite the way it sounds, no, there is no way to get it "tangled" or have it "choke" the donating diver.
A seven foot hose is routed exactly the same way, but the excess length is then tucked into the cummerbund (or waist strap) of the harness/BC on the diver's right hip. Seven feet allows a pair of divers to leave a location in a single file during an OOA... Which is important to be able to do during cave diving or wreck diving... But the skill can be beneficial to divers of even the most basic caliber.
A six foot hose is a sort of "halfway point" between the five footer and the seven footer. On really short people, the seven footer allows for too much slack in the part that wraps around the diver, and on really tall people the five footer may actually dig into the armpit of a diver that doesn't tuck.
...The bottom line is that seven feet is the standard, and the solution for diving in all sorts of situations. If you can't tuck, then consider a five footer if you're under 6' tall, and a six footer if you're over 6'. If you can tuck and you're under 5'4", consider the six footer.
I hope that clears it up. See
http://www.deepsouthdivers.org/DIR3-3.wmv for more information.