James Sweet wrote:
I'm working on a generator for someone that recently just quit producing
electricity.
Generators don't produce electricity they convert mechanical energy to
electrical energy.

On the label it touted the fact that it's a brushless
alternator; this is actually the first time I'd worked on one but I was
expecting much more inside it, certainly some sort of regulator module
but in fact it seems the only parts are a stator very much like that of
a large induction motor, a simple 2 pole armature with a diode mounted
to a heatsink, and a capacitor connected to two of the leads from the
stator. The capacitor is open circuit so that's an obvious problem,
diode checks out fine as do the windings so I'm assuming replacing the
cap will get it going.

So replace the capacitor and find out.

What I'm curious though is how exactly does this thing work?
How do you think it works, you turn it and the magnets move and break
electrons free from their atoms and that creates a charge and therefore
electrical current.

The
armature has no connection at all to anything.
Maybe the armature is broken.

I imagine it must receive
power through induction but how is the output regulated?
You said generator not transformer.

Is there a
trick to manufacturing these? Given there's no brushes or slip rings I'd
have thought all alternators would be made this way unless there was a
disadvantage.

That generator sounds broken beyond repair.