Well if you do that, it will be able to test if that is the issue.
But it isn't a fix, as your car will not shut off.

It seems like you need to route a new blue wire to the alt from the relay directly.

but I think we might back up a little.

so the blue wire coming out of the bulkhead connector is supposed to be 12 volts.

This line supplies 3 things.
The VR- sensing line.
Alt- Other field line
Ballast resistor- 12 volts during running that the ballast turns into 8 volts or so.

How you wired the relay will help determine where the drop is.

You should have cut the blue wire coming out of the bulkhead.
Wired that to trigger the relay and the output of the relay should have gone to the other side/ the end of the blue wire you cut off.
If that makes sense.

If you did that and you still have that big a drop to the alt field wire, then as I said, I would just run a new field wire directly from the relay to the alt.

You can hack out the old one from your harness later to see where the issue is. It could be as simple as the connector is going bad. Or you might have some corrosion inside the line somewhere.

Since it is spliced in pretty far up, do not just leave it hanging or you will catch a dead short somewhere. unless you can find the splice in from the factory and remove that line.

That line splices in near the VR where the sensing line goes into the VR.