You do have a wiring issue. The first place I would check for the rear lights is the harness at the lift gate hinge. You will have to cut open the cover to see the wires, have lots of electrical tape ready. Before cutting, you might want to probe the brake light with a meter.
There is a ground by the right front headlight, check it for corrosion.
The cabin blower running is a short that is delivering 12V to the ground and thereby supplying the blower. The ECU only operates the blower after the AC has been on and the car shut off. It could be a fault of the relay for the blower.
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Keeping it running is better than buying new
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