If the regulator will hold the battery in the 14v range then there is no "Probable Cause" to suspect that it has a problem.
The fuse is sized to protect the wiring.
Aircraft wiring tends to be under spec'd but a 50 AMP fuse should have at least 8awg cable attached to it.
If it is only 10awg, I would not fuse it above 30A.
Fuses blow relative to the current.
The voltage across the fuse is very minimal and nearly unmeasurable with larger fuses.
A 30 amp fuse will blow at the same 30 amps in a 12-volt circuit as in a 600-volt circuit. Amps is Amps!
I might surprise you to know that a 30 amp fuse might take an hour to blow at 30 amps.
And might take 10 seconds at 40 amps. It might take 60+ amps to get that down to under a second.
Usually, you short something out and draw hundreds of amps for the 0.01 second the fuse lasts.
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When the Fuse opened the "C" (Control) terminal disconnected from the battery so the regulator lost its reference and its load tried to regulate against a few short pieces of cable connected to nothing. It just oscillates between the extremes. The Cap gives it something to work against.
I tried to come up with a mechanical analogy and the best I have is that it is like trying to drink out of a Garden hose without spraying yourself in the face. You tend to get All or Nothing. The happy middle ground is pretty elusive.
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The Ground is the reference point for the entire aircraft.
If there is current going through the skin, then there will be a voltage drop between the various ground points.
It could easily be as much as a volt under high loads.
The Engie connection should be connected to the backside of the same bolt the battery is connected to and the cable should be the same chunky cable size.
This wiring will be carrying the starter current and can be in the 200-300 amp range for a few seconds.
Note: Current should NOT be expected to flow through the actual hardware.
Steel is a relatively poor conductor.
The lugs on either side of the firewall should be directly in contact with the firewall.
NO Nuts or Washers of any kind should be between the cable lugs and the aluminum skin of the firewall.
If your firewall is steel, then that bolt should be copper.
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*** Yes, I know that there are thousands of aircraft out there that get away with redneck wiring every day for years.
What nobody ever checks is how hot the various connection points get after cranking the engine for 10 seconds.
You would be surprised!!! There is the correct way and there is what you can get away with.
