Radiator fan stuck on and on high in ignition and with engine running?

Hello, so you're sure the DME(ECU) is in Limp Mode (or fail-safe mode)? Not sure what Merc calls it. I would check your live data for the engine computer, see what the coolant sensor is reading for temp and voltage, and also check to see if there is an AC pressure switch that is reading high, I will go through the wiring diagrams and see if there's an AC pressure switch or 3 wire sensor.
And what harness do you have disconnected? A loss of communication with an engine computer can cause the fan to run on high all the time as a default strategy, you might have communications with a scan tool if it communicates on a different network than the rest of the modules. Also did you try a full system scan to see if any modules are offline or have codes stored in them? It's good you have a scope, maybe take a look at the network waveform for any corrupt messages, but this also I will have to look at some wiring diagrams as well.

If you have the ECU unplugged right now, I would take a look at the Can Bus network with it unplugged and then plugged in and see if you noticed any differences in the waveforms. The engine is listed as having its own Can bus which then communicates to a Gateway Can bus that has the Data link connector on it, unfortunately there are no redrawn wiring diagrams for this year, only the OEM wiring diagrams. But if the ECU is unplugged, the fan will default to high speed, at least that's what I have seen in the past. But don't rule out an input causing the fan speed to be high as well.

What's the rest of the B1340 code? Because according to your live data there's no request for the Fan to be on by the engine or HVAC system, the Refrigerant pressure is only 58psi and the temperatures are not in a range to run the fan on high, so I would look more into that B1340 code, I think this communications Error for the AC system Bus is where to concentrate. The fan might be default in this case as well if there is a loss of communication because the control module may not know the Actual pressure or temperature of the system and have the same effect of a loss of comms with an ECU, defaulting the fan on high to protect the system from damage since it may not have accurate or any data from the control module.
I looked up the B1340 code and all data doesn't even have it listed, and there are only OEM wiring diagrams, which makes it more difficult to identify the correct wires. But the Can bus wires will usually always be a twisted pair of two wires, since they are communications wires.
This is the direction I think I would take with this diagram, on the wiring diagram the N22 module is the Air Condition Control module (diagram 7).

I did find a diagram with the Sun Sensor (4 in total), just looking through for a humidity sensor diagram as well. The AC Bus is going to be the Can Network that the Heater & AC system is on. This vehicle looks to have 6 Can networks. The Interior Climate control section is showing 2 different types pf fans, An Electric suction-type fan for the engine and
an Electric suction-type fan for the engine and AC with integrated control.

I am finding that if there is no output signal to the fan it will run on high, very high as a default mode. So, with seeing your scan tool data of 0% Request if the engine is running, that's the cause of it switching to high speed, and just staying on, Thats the same function I've seen other vehicles do to protect the engine from overheating.
Is the live data of the Coolant Temp sensor of 16c when the engine is running?
There is also supposed to be a TSB for a fan harness update which I'll look for.

You mentioned a voltage reading around 5-volts, was that a square wave looking signal on your scope or just a straight 5-volts?

Because if the pwm signal was coming from the ECU it would be a pulsed signal, but the ECU is reading 0% request, so it might be a 5volt reference shorted to the fan control wire. But it seems odd that there are network codes as well, the interior climate control function diagram shows the right front Sam module controls the fan from various inputs.

But heres the Sun Sensor and Humidity sensors locations. But I would monitor the network and look for any message packets that look distorted, see what the oil temperature sensor is reading as well. But the fan is running on high because its missing a signal, or at least the ECU is not seeing any signal from your scan data.

Yeah that doesn't sound right, I've been trying to find a wiring diagram for the fan in different locations, nothing yet, I'll keep looking, but without it pulling fully to ground, and I would expect the fan to be a pwm of 12v to 0 not only 5volt,

but service info on the fan operations is stating the ME-SFI control unit indirectly actuates the fan through the engine/AC electric suction fan control unit. So, the control signal from the ECU might be a lower voltage signal but I would still expect the signal to pull fully to ground. Maybe there is a bad ground here somewhere, and the fan is defaulting to high speed because the fan suction control unit is only seeing a voltage level averaging 5-6volts.

The next section states "The status of the air conditioning or automatic air conditioning is transmitted from the instrument cluster via the CAN to the ME control unit. The fan specified speed is dependent on this status".

Theres a harness section (diagram 3) you can check, it came up as a diagnostic location.
There is also a connector pinout diagram for the ME-SFI control unit and the diagrams for the fan engine and AC with integrated control unit, which Ill post these diagrams as well.
It does show the grounds which you can check. I'll post these next.

Here is the wiring diagrams for the ME-SFI control module and the fan wiring to it with the connector and pinouts for the ME-SFI (ECU).

Well, I see a red, brown, green, and is the last wire black?
And are there 4 pins in the female side of the connector?

Yeah, I've been getting the diagrams and info for a 2003 Merc Benz CL 55 AMG V8 5.5L.

I wasn't able to find any TSB number listed for this vehicle, do you have the TSB number for that extra fan harness?
I would load test those grounds and make sure they can carry a good amount of current, this could just be a bad ground, especially on a vehicle this old. And they need to be more than just a visual inspection, it needs a good load test with at least a 4 amp test light to be sure they aren't breaking down under heavy load.

You don't know how refreshing it is to have someone who uses a scope. Thats really great, so you're saying the 5v Ref for some sensors is now only 3volts? Or what reference voltage are you referring to?
Sorry about the ground locations, they were on this list, but difficult to see,
These are the grounds for the ECU diagrams section that listed the fan as well.
If a bad sensor is affecting the 5volt Ref, and that ref is shared with other sensors internal to the ECU, it can cause strange symptoms, usually a sensor shorts out and just pulls the 5vRef to ground, which can cause the ECU to completely shut down.
So, your scope is set to 1v/div, so the signal is riding on 5volts, with these small jumps of 0.8v every 100ms, and this is happening on the red wire?
The grounds listed below are all Brown wires, just fyi.

Check some other 3 wire sensors on the engine to see if anything else has a low reference voltage, being at 3volts is very strange, that almost makes me think there might be something wrong with the voltage regulator, then again you said the vehicle runs fine, I'm going to message a tech that works on Euro vehicles all the time and see what he thinks about the fan, the problem is these wiring diagrams are terrible,
You scope waveform looks like that wire is possibly shorted to a 5volt wire or a bad ground can cause elevated voltage.
I did find this small flow chart for the "Suction Fan Control Module- Short to Ground" (diagrams 3-5), and then there is also a section for short to power, but its the same exact flow chart. It does say that communication is required which you have a code for. But service info lists every code as being a "P" code and not B, I don't know if that's something to do with that specific scan tool communications or not.
Part of the flow chart on pages 2&3 mention an Actuation test of the Fan, which is going to be a bi-directional control, and probably monitor the Fan speed data PID while doing so,
Diagram 6 shows a list of the different Can networks in the vehicle.

But I think the real issue is a loss of comms with the ACC pushbutton control module (N22) since the sun sensor and the humidity sensor both input to that module, and that might be why they are setting B codes, and not powertrain codes.
The ACC control module looks like the control head for the heater and AC.
Thats the main unit at the top of the HVAC wiring diagrams (#8 below) N22, very in-depth system with a ton of modules.