The 76 is supposed to power the fuel pump when you have the ignition in the START (cranking) position. NOT in the ON position if the engine is not running. Once the engine is running a switch in the AFM keeps the fuel pump powered. It's annoying, but it's a safety thing. Shuts off the fuel pump if no air is being sucked through the AFM. I guess they don't like to see a fireball if it can be prevented...
Definately get the 76 280Z FSM from carfiche... It tells all about that stuff. My son has a 76. We swapped out the L28E for an L28ET a couple of years ago.