Aa Perm
Headlights on exactly one side and every edge already solved: three corners cycle. Aa and Ab turn them in opposite directions.
R' F R' B2 R F' R' B2 R29 moves · Probability 1/18 · Corners UFR→UBL→UBR→UFR · Mirror: Ab Perm
Setup: apply these moves to a solved cube to reach this case
R2 B2 R F R' B2 R F' R