Fuel pump relay
I have a '85 500SEC. I've posted a number of times on this subject.
My car would shut down at the oddest times. And it would not re-start.
I finally discovered a bad solder joint on the relay.
I even picked up a replacement and it also had the same bad solder joint.
Just open the relay(s). Check the larger of the two solenoids. The back side of the circuit board. The main support for the coil of wire, that is the solenoid, is also the ground. If you see a dull gray solder joint and maybe a circular crack this is your culprit.
Re-solder the joint, trying not to overheat the circuit.
Mine has not missed a beat since I did this. It took all of 15 min. to fix.
Good luck, John F.