It's most likely a bad brake light switch which can cause the exact symptoms you describe. At least that's where I would start. Get a genuine MB one at the dealer. They're not very expensive and pretty easy to change. The hardest part is getting the trim panel below the steering wheel off.
A bad BRAKE LIGHT SWITCH has exactly these symptoms, especially if it's intermittent. Look for the sticky - one guy does it without taking off the trim panel (saves 30 minutes and likely light damage to the panel). You're working almost blind, but if you lay on your back and look carefully how it's fit, reach up with your LEFT hand (trust me), squeeze the retaining clip on the switch shaft (look at your replacement part to understand it), then turn CLOCKWISE, it will come out. Carefully unplug it, plug in the new switch, and install it carefully. Make sure your battery is unplugged or at least your key is not in the ignition. Cailbrate the plunger of the new switch a few times by pressing the brake pedal a few times BEFORE you insert your key and start.
Please report back on the fix. Personally, I wouldn't mess with ABS until you've replaced the $30 brake light switch.