The system if it's GM's is fairly simple. The engine runs off of the drivers side tank iirc, and the right side tank gets pumped over into the left side tank. Once the level in the left tank reaches roughly 3/4-7/8 of a tank, the ECM will trigger a transfer pump to move fuel from the auxilary tank to the primary tank. It will stop the pump once the level goes above the 7/8 mark roughly. The ECM reads the level sensor from each tank, controls the transfer pump via a relay mounted in the underhood fuse panel(this is how pickups are done, BURB's have an auxilary relay outside the box for it), and it also outputs a fuel level amount over the class 2 j1850 data bus for the cluster to then read and display. If there are any problems in the system, the ECM will default the gauge to empty, and not run the transfer pump. Faults that can disable the system are a level unit that stays when the ECM expects movement, if it detects fuel being transferred when it shouldn't(try filling one with the engine running, the gauge will plummet to empty and stay until you shut it off and restart it), or eratic readings from a level unit.
As far as I know, GM only used left and right saddle tanks. You say rear tank and no mention of the gauge going to empty, sovthis is sounding like an added on system, in which case you're pretty well stuck trying to find where somebody put it, and how all it works.