Surely you already check the fuse , next would be to find the pump relay check it for operation, if working properly, check plug at pump assy on tank for pump power, one will be hot all times key is on this is gauge wire, one wire should come on hot for a few seconds when some one cyles the ign key off and on. this would be the same as the time the relay is on.
Most commong reason on the 1979 and earlier models is dry rot on the fuel lines. When the rubber is 40+ years old it tends to leak. Another common problem is the fuel filter being installed in the engine compartment. Most fuel filters are installed above the distrubitor when they begin to leak they leak directly on to the distrubitor and the spark starts a fire.
The whining noise is a common sound and problem with all Chevy trucks and suvs. Yes it is the fuel pump and it does not mean the pump is going out. Chevy recommends to keep the fuel tank 1/2 full at all times to keep the electric fuel pump cool. I've installed many NEW fuel pumps and they also whine/ make noise. It is just a common problem. If you are concerned about the fuel pump then you need to check the fuel pressure with a fuel gauge.
Your pickup is a fuel-injected vehicle versus an old carburetor type. By running the vehicle out of fuel, you have air in the fuel lines and the injectors. The fuel pump cannot push out the air which is causing your problem. I'm sure that if you had a repair manual, it would explain the proper procedure for bleeding the fuel lines. The same problem occurs with diesel engines as well.
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