Electrical loads that have a switching power supply will draw less current as the voltage goes up and will draw more current as the voltage goes down. Examples are modern avionics that are designed to operate on 10 to 30 volts. I have read about a strobe switch that got hot, even though the strobe kept on working. Evidently that strobe has a switching power supply. When the defective switch dropped voltage, the strobe compensated by drawing more current, which made the switch even hotter.
It seems unlikely that a fuel pump would have a switching power supply. I conducted an experiment with a spare Facet 40105 fuel pump. I ran it with a 12 volt battery and measured the current at about 3/4 of an amp. Then I switched to a 6 volt battery. The pump still made noise but it quit pumping. The current dropped to about 1/2 amp. The 3 amp fuse in series with the pump never blew. I know the experiment did not duplicate the conditions in an aircraft. But it seems to me that the fuel pump does not draw more current when the voltage drops. Maybe the avionics cooling fans, that are on the same circuit, caused the fuse to blow. This is a good example of why each electrical load should have its own fuse. A discrete fuse for each item would make troubleshooting much easier. An even more important reason to have a separate fuse for each load is to prevent a bad component that blows a fuse from disabling an unrelated component.