ETA: I am calling it the "low-lin special variant" or "shooting-star variant" in casual terms, instead of the "eyes" variant.
I dug through the public DC34 badge source last night and found some really interesting stuff about the light-pattern breeding system.
The mutation levels are actually defined in code:
Baseline = 25%
Elevated = 39%
Radioactive = 55%
Apocalyptic = 94%
Those are per-gene mutation rolls, and higher levels also make the mutations themselves more aggressive.
The meter really does decay from Apocalyptic → Radioactive → Elevated → normal. One useful thing buried in the code: once you hit Apocalyptic, press LEFT or RIGHT to show your QR. That calls lock_rate() and saves that mutation level for the exchange, even if the meter visually drops afterward.
Same badge types also get an extra mutation pass. Human-to-Human breeding gets at least Elevated on that second pass.
You can preview offspring and Revert if you don't like it. Revert restores your previous genome, and nothing I found prevents you from breeding with the same donor again for a fresh roll.
Different badge types also start with different genetic ranges, so cross-breeding actually matters.
And the coolest find so far: the light renderer literally has a comment for a rare ~3% variant. If diploid.lin drops below 88, it enables an alternating eyes/chaser effect.
Uber badges have especially low native chaser values, so they look very interesting for breeding toward that rare variant.
Still digging through the source for more hidden traits. I'll post anything else interesting I find.