If you have a spare fuel pump relay you might try swapping it. I'm not sure if yours has a separate relay or if it is built into the MAS relay. The older cars had a separate relay.

I'm wondering if your relay is actually energizing the pump when you turn the key to on, or only when you crank the engine. Also, the system is built to keep the pressure up when the engine is off. If it's leaking down it will be hard to start.

Surely a search would reveal a lot of info about this.

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2012 E350
2006 Callaway SC560