here's something to check: pull off the passenger tail light assy and check the condition of the wiring on the pass through out of the trunk. There's a bulkhead connector that is all potted up. On my old coupe, my brake lights and turn signals were acting funny. The wires on the bulkhead connector were corroding to the point where I had a sneak circuit, I would step on the brake and the voltage would come back up through the tail light circuit, through the headlight switch, and turn on the fog lamps! I ended up cutting and splicing the wires on the whole taillight / brake wiring harness.
Take the dielectric grease off, that's OK for high frequency / high voltage (spark plugs) but at 12 volts DC it's an insulator.