Its no problem, mama always said patience was a virtue.
Anyway, I finally found a pic in the Chiltons of the 3.8 engine bay. I do see what youre talking about. But while I was thumbing through that book, I noticed something else.
It has a procedure for "Low coolant indicator ON with coolant level OK"
1. Disconnect the engine coolant level indicator module at the radiator (pictures show it on the left side of the radiator looking from the front, just below the fill cap)
2. Place the ignition switch in the On position, check if the low coolant indicator is on.
3. if indicator is no longer on, replace the coolant level indicator module.
4. if indicator is still on, check the circuit for a short to ground, between the instrument cluster connection and the module connector terminal B (usually a yellow/black wire to instrument cluster)
5. If circuit is ok, instrument cluster may need replaced.
Now, heres what I make of that. Apparently you have a sensor/module on the radiator that reports the coolant level. What the Chiltons doesnt show is that the 3.5 uses a different cooling system, and that the sensor is in fact on the overflow bottle. So I mislead you in that respect because I thought thats where it was for all the W-bodies.
The pictures show it as a small squarish sensor plugged into the side of the radiator. They say it is on the radiators right tank, which should make it on the left side if youre facing the car.
here is how they say to remove the sensor, the stuff I just typed is to tell if the sensor is bad or not.
1. partially drain the radiator to a level below the sensor.
2. unplug electrical connector from sensor
3. the sensor is retained with a snap clip, to unlock the sensor lift one leg of the snap clip from its locked position and pull outward with a slight twisting motion.
Installation is reverse.
I wish I could help you more, but Ive never done this, and never even heard of many people having to do it. Plus my car seems to use a completely different setup, so I have nothing to look at. Im going to go have a look at my own car, and see if I have anything similar.
I would also like to apologize if for any reason you decided to rip out the airbox assembly and overflow bottle only to find the sensor is not there
Id be pissed at me personally.
EDIT: I did some digging on RockAuto, and was able to locate the coolant level sensor for your car, but couldnt find one for mine, so thats no good haha. But it was a 40-50 dollar part after shipping from Rockauto, so probably even more from a local place. I wanted to see if they were different part numbers, but it seems mine doesnt exist.