When I diagnose a problem like this I find the cost of the part ($70+/-). Then I look at how complex the system is. I say to myself, which is cheaper, the part or the labor cost to diagnose the problem. I then do which ever is less. I can say that the fuel pump relay system is more complex than it looks. It requires an o'scope to do it right.
Now If I had the car, I would put a relay in it. Actually, I would resolder the circuit board first. I had the problem on my 500SEL about 10 years ago, resoldered, and still going.

Paul

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84 500 SEL (307,xxx miles)