See my random thoughts and remarks interspersed below...

First, dumb question because I'm not familiar with C3's: do the rear
side markers go on with the tail lights? Do they blink with the turn
signal and/or brighten with the brake lights? I expect they aren't
supposed to blink or brighten, but I don't know... ie, is it possible
you're looking at the wrong bulb or fixture for your problem?

I spent some time today thinking about it myself, without pinpointing a
logical suspect.

You don't really need to replace the ground, you can just add your own
makeshift ground wire clamped to a housing bolt and a good frame ground
for testing, or use a multimeter to check for zero-ohm connectivity
between the socket housing and a clean frame ground. If there's a wiring
connector behind the socket at the tailight, disconnect it and use a
multimeter to check at that point.

More food for thought.... check my interspersed remarks below, in no
particular order...

I would think so, too.

So the brake lights and turn signals work with the headlights off; the
parking/tail lights work with the headlight switch on, but then using
the turn signal and/or brake light switches, nothing works on the left rear.

The "brake light filament" is also the "turn signal filament", and based
on the wiring diagram on my C2: each side of the rear is fed by a
separate terminal on the turn signal switch (each tailight group on
mine... right versus left; you have only one tail light on each side but
a rear side marker is probably coupled to each tail light); likewise the
turn signal indicator lights in the dash are fed by a pair of terminals
(separate from the pair that feed the tailights) and the same terminal
feeds the front parking light.

Do the front parking lights operate normally as turn signals? Does the
left turn signal indicator light in the dash operate normally even when
the headlight switch is on or does it hang up? I think you said the
front turn signals are OK, so the dash blinker probably works, and the
problem, it seems to me, has to be in the turn signal switch or in the
wiring from it to the left tail light, but there's still that nagging
fact that turning on the headlights is what screws things up.

Here's a way to at least narrow it down, I think:

Locate the body harness connector going to the rear of the car. I'm not
sure where it is on your car, but I think it's probably above the side
kick panel up near the fusebox and close to the front door.

If you find it and disconnect it, you could use a DC setting on a
multimeter (from a pin/socket to ground) to test the wires coming from
the upstream half of the connector (ie, from the headlight switch and
from the directional signal switch). On my C2, the power wire from the
headlight switch to the tail lights is a black wire, the wire to the
left rear brake/turn filament is purple, and the one to the right rear
brake/turn filament is violet. In any event, the wire to the rear
parking/tail light filaments will have 12v only when the headlamp switch
is on; then (with the headlamp switch off) you need to find the two that
have power only when the brakes are depressed, ...and then each of the
two will pulsate when the corresponding turn signal is used... now that
you have them located, you can check those two with the headlamp switch
ON. If the left one ceases operating, at least you'll know the problem
is upstream and not in the harness wiring to the rear, or vice versa.

If the problem is downstream, we still have to figure out how turning on
left turn/brake affects only the left rear running light since the
running lights for both rear tail lamps are on the same wire.

If the problem is upstream, we got more thinking to do... I'd vote for
the turn signal switch since it's a common factor linking brake light
and blinker circuits, except I haven't yet figured out how the headlamp
switch affects it, either. Can we assume you're using the correct bulb
and that you've tested it in the right-hand tail light?

 Some thoughts:

Try a test ground wire from the wiper ground connection to the battery
negative post (disco the current ground wire first) and then check the
wiper and stereo operation.

Is the stereo normally turned off, or do you normally leave it on so it
just starts playing when the ignition comes on? If it was an aftermarket
stereo, maybe you need to revisit the connections for the hot and
ignition switch leads at the radio to be sure you don't have them
reversed, and revisit the wiper ground wire to make sure it really does
connect to ground at the other end... and test that disco'd ground lead
to see it it's hot.

Does the antenna raise and lower normally?

That the stereo comes on means you probably have 12v getting to it's
switched ignition wire... could you have accidentally soldered across 2
wires (or as I said before, have the switched and nonswitched power
leads reversed)? Disco the stereo for the time being and see if that
changes the wiper and/or tail light behavior.

Would it be difficult to disconnect those two devices (stereo and wiper)
while you're troubleshooting the current problem? You didn't mention
whether the tail light problem or the wiper problem occurred well after,
or immediately after, you added the stereo.

No. I don't think so, but I haven't fully traced even my C2 wiring diagram.

missing ground for the socket.
********
Well that's what I *first* said. That type of problem is almost always a
ground problem. But the OP said he had checked, cleaned, & rechecked the
ground.
Then he said that BOTH the brake & taillight was lighting up the SAME
FILAMENT...
(try to keep up :-)
~ Paul
aka "Tha Driver"

Giggle Cream - it makes dessert *funny*!