Put the new lights in. Bit of a faff, but not too bad. No need to remove the bumper cover if you have long skinny arms.
I was able to smoke the broken one apart by running a bead of Goof Off around the seam, letting in marinade for a while, and then carefully prying.
The Goof Off melts the gray back plate, but not the lens. A little messy, but effective.
The circuit board has a diode, a 140Ω resistor, and 2 LEDs, all in series.
One end of the resistor has come unsoldered.
I think I can fix it. It'll take a good soldering iron, good eyes, and a steady hand.
I have a good soldering iron.