...disconnect the battery positive, pull the EHC connectors, clean them thoroughly, put fresh di-electric grease in...
1+
Same-same, you want anything but air and water touching the pins. Why? Eyes gots me 3 basics down.
1.
Magnetic field throughout the wire.
2.
Heat cooks the air at the pins.
3.
Chemical reaction are the green/white leftovers on the battery posts, pins, wire is pull the wire back and see the green near the copper wire ends for example.
WATT would cause my battery to die after being in a downpour? Condensation is now air has a corrosive buddy gone green. A water drop is hello other pin and now a conductor to transfer a hot pin [key off], to a jobber is ground or it shorts, right? So dead battery it is.
But if you had vaseline smashed in between the pins is water is not going to find a path is more roll off the grease. No condensation to cause green male to green female pins is now it's a green-green contact and dead is the good Ebox you go swapping a good know pin = Chem Reaction... think preventive maintenance.
Let me get that photo correct, xx. Do I see lit LED lights replaced by pins? So you cannot install a connector there like you can the other side without LED's? And how is A-B short with or without power is how are you reading this? Are you seeing a burnt part or that square black thing thru the bake? Where are you seeing a short, black burnt area, raised [over heated] bake, etc?