You don't have a J-valve on the manifold pictured. (I do want to correct myself; there is a seat on the center section, what type of seat you will find depends on who made it. It may be hard to find a replacement seat)
A standard J-valve will have 1 to 2 O-rings depending on the make. If the design is one that is accessed from under the on/off knob, then there should be a bonnet under the knob that will screw off. There is usually an O-ring sealing the bonnet and a 2nd O-ring sealing the knob shaft to the ID of the bonnet. An older UDS manifold with a J-valve may have a parts that are accessed from the other side after disassembly of the manifold using an allen wrench .
Inside of the J-valve is a spring loaded seat with a Mechanism to pull it away from the seating orifice. When the J-valve is UP, the spring hold the seat against the orifice and tank pressure pushes the seat open. The seat will not seal until the tank pressure falls to a lower pressure. Depending on the spring, this will be in the 300-500 psi range.
When the When the J-valve is Down, the seat is pulled away from the orifice and you have access to the remaining air.
Now with doubles, remember that the J-valve only works on one tank. By the time you have reach the hard breathing and turned the J-valve, the other tank will be at about 100-150 psi depending on how your reg works and what the IP is set at. If you are using a single stage like a Mistral, the other tank could be down to the water pressure.
In other words, the J-valve on a set of doubles will give you the exact same reserve volume of air as a J-valve on a single tank of the same size.