Another bad voltage regulator?

After digging around the wiring for a while I don’t see any major issues with anything. I don’t feel like removing the factory “loom” from everything so I think I’m going to install a relay to give the Vr the true battery voltage it needs. Does it matter which pin on the Vr gets the full battery power? Both wires in the Vr connector have about 1v less than the battery when the engine is not running.