Uh oh, electrical gremlins - headlights not working; hole burnt by plate light?

[Y-me]

13 RT SE5 weirdness at ~41k miles.
One headlight fails, okay time to do the bulbs.
Got the replacements but when moving the Spyder around to change it notice the other bulb is out.
Okay, could be the bulb was on the way out too.
The high beam relay sounds fine when pressing the high beams but still dark lights.
To make sure it's not a relay, without having spare relays though, I swap the hi and lo relays with no change and put them back, and the headlight and the 12v DC still with no change, so I put them back.

Then I see what might be the cause when I go to the trunk to get the bulbs.
Something has burned a hole through the plastic just above and to the right by an inch or so of the plate light.
The plate light works okay, the trunk is open sensor works, and the brake lights work.
She starts right up, no funny lights or other drama.
Usually, the computer is sensitive to shorts like this.

Anyone have an issue like this?
Could a short like this take out the headlight bulbs?
How do you troubleshoot this?
I was thinking of pulling the bulb for the license plate light to see if the headlights magically start to work again but it's possible that the short killed them.
What might I be looking at for a repair provided I have to take it to the stealership?

Sorry for the long post, thanks in advance for any and all wisdom on the matter.

Y