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That's not a relay. It's just a resistor that excites the alternator field to start the charging process off. It's not connected to the starting circuit in any way.
The device that you are focused on that has the appearance of a relay is what's called the "pre-exitation resistor" as pointed out by an expert earlier in this thread, and as advised has nothing to do with the starting circuit.This post. My post is my issue. I need to get a new relay. I'm pretty sure it's a relay not a resistor like someone said. The big long post you linked talks a lot about lots of things. But not this exact relay. So, that big post is not my problem, this post is.
With LED's replacing the old incandescent charging indication lamps this pre-exitation device is needed - the current from the old lamps provided the excitation current.
The response you get from tapping on that device is an indication that there's a poor electrical joint somewhere in the fuse box.
The only place you'll be able to get that pre-exitation device is the dealership.