Let's see if I understand:
Probe terminal 85 (wht/blk). it should be hot all the time. Wht/blk-hot
Disconnect the wire (gray/wht) that goes from the oil and temp switch to terminal 86. Make sure the wire to the relay is not touching ground and is not connected to either sensor. Probe terminal 87A (org/wht) - it should be hot. Probe terminal 87 (lt blu) - it should be dead. Blue - dead, Orange/wht-dead
Now temporarily ground terminal 86. You should hear the relay click. Terminal 87A should now be dead, and 87 should be hot. The check engine light should come on. With 86 (gry/wht) grounded both 87's have power..
Is that what you're seeing? both 87 and 87A are dead, then when you ground 86 they both go hot? That's an issue - not how the relay is supposed to work....