The connector from the handset LOOKS like an RJ connector. It is the same type connector, but the pinout is special for your phone. It is not an RJ connector with a standard telephone pinout.
I will be surprised if there is an RJ11 connector anywhere on your phone for modem or fax use.
My '96 E300 had a Motorola integral "factory" (actually installed at the port of entry) phone and it had no RJ11.
Besides, they put that blasted steering wheel in there, and it was really in the way when I was using my notebook computer.
'84 Euro 240D, 516K miles
'88 300E 5 Speed
'81 300D Daughter's Car
Over 800,000 miles in