Ab Perm
Headlights on exactly one side and every edge already solved: three corners cycle. Aa and Ab turn them in opposite directions.
R B' R F2 R' B R F2 R29 moves · Probability 1/18 · Corners UFR→UBR→UFL→UFR · Mirror: Aa Perm
Setup: apply these moves to a solved cube to reach this case
R2 F2 R' B' R F2 R' B R'