Testing Cooling Fan

Hi guys,
While troubleshooting issues with the AC (after refilling the gas without any significant improvement), I have noticed that the seems to work much better (to not say only) when the car is moving. As soon as the car is stopped the AC compressor stops quickly.
I have noticed that the cooling fan does not start with the AC, and suspect it to be the root cause (also because last year I had a warning while blocked in a traffic jam).
I have checked the 40A fuse of the fan it's ok.
I have tried to remove the connector of the fan (to try injecting 12v directly in the fan ), but didn't succeed.
Any advice to access and unplug to that connector ?

I have also seen in the service manual that there is a manual diag procedure , that includes testing of the cooling fan, but didn't succeed to enter in the test mode.

I successfully recently tested another procedure for testing the AC controler, but I'm blocked with that one.

Here is the procedure (PCS-15)

Diagnosis Description INFOID:0000000005914120
In auto active test, the IPDM E/R sends a drive signal to the following systems to check their operation.
• Oil pressure warning lamp
• Front wiper (LO, HI)
• Parking lamp
• License plate lamp
• Tail lamp
• Front fog lamp
• Headlamp (LO, HI)
• A/C compressor (magnet clutch)
• Cooling fan

Operation Procedure
Never perform auto active test in the following conditions.
• CONSULT is connected
• Passenger door is open
1. Close the hood and lift the wiper arms from the windshield. (Prevent windshield damage due to wiper
When auto active test is performed with hood opened, sprinkle water on windshield beforehand.
2. Turn the ignition switch OFF.
3. Turn the ignition switch ON, and within 20 seconds, press the driver door switch 10 times. Then turn the
ignition switch OFF.
4. Turn the ignition switch ON within 10 seconds. After that the horn sounds once and the auto active test
• Engine starts when ignition switch is turned ON while brake pedal is depressed.
• Only a vehicle with the vehicle security system, the horn sounds.
5. The oil pressure warning lamp starts blinking when the auto active test starts.
6. After a series of the following operations is repeated 3 times, auto active test is completed

I have tried many things (with or without the engine on, with the driver door opened or not, using the switch of the door, the door lock button outside, the door lock button inside ...) ... but no success :-(
answering to myself , this could help people others:
when you have an ignition stop/start button (intelligent key), the procedure is:
1) open the driver door
2) press 5 times the ignition button
3) press 10 times the contact switch of the driver door
4) press 3 times the ignition button

in my case the test is ok except that the cooling fan does not operate (just hear the relay clicking) ... so back to my initial issue, how to unplug this damned fan connector to test the fan motor directly