You can try replacing the brake light bulbs. The system is very sensitive and mine was triggering intermittent bas/esp errors when I had a headlight bulb that was going out. I didn’t find it until the bulb blew out. Changed it and had no further problems. Since yours seems to be triggered only when you hit the brake pedal it must be something in that electrical system. It is also possible that you got a bad brake light switch from MB. I don’t recall ever seeing a procedure for testing them - just replace.

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07 E350 4Matic wagon, 06 S430 4Matic, 99 SLK 230
retired W210 (x3), W124, W126