Fuel Pump
Based on the beat up and corroded condition of the existing fuel pump, and other parts on this car, 
I can only speculate that it's the original pump from 1984. Sure, it was pumping just fine, but it was also weeping, it was probably tired, and I was already doing the fuel lines.
On the 305ci LG4 of this era, the fuel pump is mechanical, and located on the front right side of the engine. The front of the camshaft has a special lobe that activates a pushrod. The pump is just a diaphragm inside of an enclosure, and that pushrod fights a spring causing the diaphragm to pulsate (pump).
Changing it seems pretty straightforward, just 3 fuel lines and two bolts... but not so fast!!... Remember that pushrod? When you remove the fuel pump, that pushrod slides down occupying the space where the pump lever once was. When you install the new pump, the pushrod will be in your way. So just move it you say... yeah, good luck with that. It's a slippery little thing, and there's not much space to work, but there is another way.
On the front of the engine, you'll find a small bolt that seems to serve no purpose. Even removing the bolt tells you nothing. 
The removal of that bolt opens a passageway that lines up with the side of the fuel pump pushrod. If you position the number one cylinder at top dead center of the compression stroke, remove the mysterious bolt, and thread a longer bolt in its place, that bolt will stop the pushrod from sliding down. Now you can safely remove and reinstall the fuel pump without having to fidget around with the pushrod. Here's a tip, you can even use one of the fuel pump bolt. video here
This fuel pump has 3 lines, fuel in (3/8 rubber), fuel out (3/8 inverted flare metal), and a return line (1/4 rubber). The return line sends excess fuel 
back to the tank, stabilizing pressure, and avoiding vapor lock. Without this cycling back, the fuel can heat up, vaporize, and restarting the engine can be challenging, particularly in warm weather conditions. more here
Once you've got the pushrod dealt with it really is just a matter of lines and bolts. Grab a 7/16 wrench and do your thing. Once the old pump is off you must clean all the old gasket material off of the engine block. You can use a solvent, but I usually scrap with a razor, and hit it with light sandpaper. Putting the pump back on is just a reversing of the steps, but don't over tighten. People are always temped to crank it on, but 30lbs will do the job.
Try as I may, I couldn't find an OEM pump. I ended up finding this Carter from RockAuto. 
It was supposed to be a direct replacement, but it wasn't and that created two new issues. First, the metal line going to the carburetor was ever so slightly out of alignment, requiring much fiddling around. Then the pressure was too high (7-9lbs).. these old carburetors like to stay below 6lbs. The additional pressure forced fuel past the seat, which was causing the carburetor to flood. Apparently this is quite common. Now it would seem that I need a fuel pressure regulator... I wish someone had told me before I wasted a bunch of time and energy figuring it out. pump here