Still would look at fuel pump relay.

The device mechanic suggests is called electrohydraulic actuator (EHA), and it would be interesting to search this forum for descriptions of possible failure modes for this item. Only one I'm familiar with is that it can leak fuel, which doesn't mean car stops running.

When a motor suddenly stops running it's VERY likely not getting fuel and on this car it's very likely the fuel pump(s) and it's VERY likely they're not getting power.

Ignition systems on these cars are VERY powerful and VERY reliable and sudden failure seems unlikely.

Fuel pump relay failure happens a lot.

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Kent Christensen
Albuquerque
'07 GL320CDI, '10 CL550. '01 Porsche Boxster
Two BMW motorcycles