I don't have a ton of experience with the CIS and quirks, but for electrical, if your fuse socket shows melting then you have a Current flow heat build up issue.
I have seen that quite a lot on different cars, planes, and computers/lcd panels.
Typically it is a sign that you have resistance in the circuit, in cars and things it is usually due to corrosion/cold solder joints.
in the Fuse panel it is good to take the ground off the battery, then remove and reseat all fuses and relays once a year to clean the connection between the fingers of the socket and the relay as there is a differential metallic corrosion exacerbated by the current of the circuit that allows electrolysis to happen more frequently. It is a good habit to do this once a year.
Fuse panel fingers are Brass, the Fuses are soldered aluminum, or copper, or the relays are copper, soldered steel, or aluminum/soldered, and the Brass reacts with the different metals at the atomic level causing the electrolysis to happen even with the car off.
Here is the only fuse that I failed to reseat on ownership and about 8 years after I got the car.
It was the a/c fuse at the very top of the fuse panel......yep missed it.
Here is the inside of the 89 fuse panel with corrosion on f1 and f2.
I know that when I have wires that get hot or show signs that they have gotten hot, I usually take the time to remove the Battery cables and clean them at the Battery and opposite ends. I know that the battery ground (neg) to the frame and the frame to engine are subject to battery outgassing and or road salt/debris, and getting then cleaned/shiny, then spraying that battery corrosion preventer goes a long way to less electrical gremlins, If you haven't replaced the Battery to frame and frame to engine cable, it wouldn't hurt to upgrade at this time.
CIS usually has a WUR warm up regulator that has an issue with corrosion. Usually I have heard this happens, and or the Fuel pump relay new with Iffy connections can develop cold solder joints as well and a lot of folks carry a spare in the glove box to prevent stranding.
I would also suggest that you clean your cable ends at the fuel pump as well. I went so far as to take mine off and clean and solder them as I didn't trust the Crimp only connectivity that the OEM's do to the wires, yes corrosion can occur between Bare copper wire and the Crimps, where cleaning and soldering prevents this in the long run.
Last issue is the condition of the Fuel pump, and is it making noises that you can hear?
I have had fuel pumps on mine whine and stop working when they overheat due to a bad in-tank fuel pump or connection hose.
You might try running a couple of tanks of fuel with MMO (marvel mystery oil) about 8 oz in the tank, it tends to clean out the fuel varnish.
Fuel Pumps when they start going bad can also do this intermittent thing.
In my case on my digifant I had a similar issue, and it ended up being a bad fuel pressure regulator that would by-pass all fuel from the fuel rail back to the tank...
It too took me a few tries to narrow it down. You might refer to the Bentley/Haynes troubleshooting guide for the CIS.