if youve still got a stock fuel system, obviously filter first. next pull the strainer down, check for it being full of trash. then pull the heater grid and look at the electrical connector between the pins. any melted plastic is a dead heater.. id never recommend putting one back in, they all eventually die and leak air. next is the sharp hose elbow from strainer to pump, they tend to delaminate in that corner and behave just like you describe, if its squishy/rubbery, its junk. i replace with hose barbs and a long segment of looped 1/2" hose zip tied up to the brake master so it doesnt rub the steering shaft. nothing can make that bend without kinking. after that id pull the fitting off the mechanical lift pump and check for a snapped spring, i had that break and also run like yours. overflow valve could probably do the same. rotted metal lines ontop the tank and old fuel hoses will too.
on an old truck with fuel issues.. i find the cheapest and fastest solution is to just drop the tank, pull the sender, and go through the whole thing with new hose from front to back.