My right tail light and dashboard light went out. Traced the tail light power issue all the way back to the fusebox, and found that the splice connector was scorched to crispiness (bottom right):

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This is what the splice connector looked like once I pulled the fuse box to pop it out:

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I cut the connector off and spliced and soldered the wires together like so:

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Everything works now, but the moral of the story is - if you have any unexpected electrical issues, even a tail light out, park the car immediately. Otherwise you're risking an engine fire, because the wiring on Aveos is so unbelievably crappy. What's amazing to me is that this is a known issue, but GM isn't publicizing it to owners: A typical NHTSA report I found:

Dec 30, 2014 - Saint Paul, MN - Electrical System
DASH LIGHTS DID NOT TURN ON WHEN THE HEADLIGHTS WERE TURNED ON. ALSO, RUNNING LIGHTS DID NOT TURN ON AFTER MY HEADLIGHTS WERE TURNED ON (FRONT AND REAR RIGHT). LEFT REAR TURN SIGNAL DOES NOT WORK. I WAS TOLD BY A MECHANIC THIS WAS DUE TO THE SPLICE PACK MELTING. HE ALSO INFORMED ME THIS WAS A KNOWN ISSUE WITH CHEVROLET AVEO'S. THIS SHOULD BE A MANUFACTURERS ISSUE AND NOT THE OWNERS IF IT IS A KNOWN HAZARDOUS ISSUE.

Unbelievable...