Definitely get the Motive bleeder (or another brand or a homemade version). I have the Motive and the 1st vehicle I used it on was a W124. The brakes felt brand new when I was done. I never got that same firm pedal pressure when a 2nd person pumped the pedal or when using the stick method (I've done that too). It is really easy to miss the rear reservoir and I nearly ran mine dry a couple of time before I got the Motive.

Factory repair manuals are readily available for your w124:
https://www.startekinfo.com/StarTek/
Index of /service

Good luck!

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