If I'm not mistaken, it's a part of the fuel injection pump. The fuel injection pump is driven by the timing belt, so it's not as easy to gain access to. I'm not sure about the exact location of the connector for it either. It could be an issue of a broken or loose wire/connector, causing the issue, or the component itself has an internal open circuit.

Knowing only the basics around my engine compartment, where would I start looking for a potential loose connector? If it is as simple as that.

It's a fault for the fuel shut off solenoid. If excess fuel is getting into the cylinders, then it would absolutely cause poor fuel mileage.

This tank suddenly shows a 30% loss in fuel economy and showing a 1537 code. Finding mixed reports online, any thoughts here or if they are even related?

30% mpg loss and 1537 code