Very difficult to take good pictures but it looks like the flexible conduit (not sure of the right term) that loops down and back up is wet with oil, however almost everything around it is dry. You can see that the "wetness" is only on part of it.

A few days ago I noticed a whining/groaning sound coming from the accessories that was accompanied by a burning plastic/electronics smell that I couldn't localize, although I smelled it both inside the car and under the hood.

Is there something that could be leaking a fluid to exactly hit just that part of the wiring harness or am I more likely dealing with a bad alternator or a short or something similar?

 

Oil on the wires won't hurt anything.

This should not happen if the wiring is stock and good name-brand fuses of the proper amp rating are used. There are some cheap fuses on the market that do not blow even with an overload, and the wires burn instead.

Once a wire has melted and shorted with other wires in the harness you have to do major repair of the harness or replace it.

 

Educational question - What can you do to verify a fuse properly?

 

What do you mean by verify?

Testing if it's opened or not is easy enough, you just measure it with a meter.

If you mean evaluating a fuse for its fusing current, a decent lab power supply set to constant current mode plus a digital oscilloscope to measure the delay between current applied and opening maybe?