Interesting. The Central Locking Pump (CLP) also is the Security System Module (SSM). The SSM does activate the lights flashing when you lock the car with the FOB. I'm not sure if it has anything to do with interior lights dimming. I would think the lights dimming in the interior is a function of the body control module (BCM).
Something you could try is looking into the interior of the car after you lock it with your FOB. In the center of the tow away alarm switch is a small red light which should blink after ten seconds or so, once the car is locked. The blinking light indicates the security system alarm is activated. Can you see the blinking light? If it is not blinking then you have a problem with the SSM and replacing the CLP/SSM may just fix your problems, but I wouldn't use a CLK pump. You would only be adding an unknown into a situation that is not working correctly.