Weird wiring for a weird car

OK, I am pretty sure it doesn't matter what specific car I have, other
than that it is a 12 volt negative grounded vehicle, with a separate
alternator, regulator, but I'll go ahead and say it... this is a 1971
Citroen 2CV.

Here are the two things I think are weird. The first may not be an
issue, because I haven't tested any other cars to see if they do the
same thing, but instinctively I think it's not right. When I put
connect a test light from the postive to negative battery terminals,
with the ignition OFF, the light lights up. When I turn the key, so
ignition is ON, but the engine is not running, the test light does not
light up. That just seems wrong to me, as if the ignition wasn't
grounded or something. But you experts tell me.

The second thing, that is more at the heart of the problem I'm having
(charging system not charging the battery) -- is this. With this car,
ignition OFF, the alternator's + terminal should have power, and
indeed, the test light lights up. And, both the Field wire on
alternator, and Field and Ignition wires on regulator all do NOT light
up with ignition OFF, engine OFF.

However -- with ignition ON, engine OFF, all FOUR of those wires light
up! -- though, I would estimate that the + terminal of Alternator and
the Ignition wire of the regulator are getting more volts than the
Field wire on both Alternator and Regulator, because the light is
brighter on the + or ignition wires.

Now, someone advised me that in that last scenario, ONLY the Field
light should be on unless the battery is discharged (granted, which
mine probably is), but I still think there's something screwy going
on.... My next step is going to be bypassing the harness and connecting
wires directly between Regulator Field and Alternator Field, and
Regulator Ignition to Battery Positive Terminal.

Any tips/suggestions/name calling?

Thank you,