Corner permutation (2-look PLL, step 1)
Put the corners in place: an adjacent swap or a diagonal swap.
What it is
The first look of 2-look PLL permutes the corners, leaving the edges for EPLL. A Jb-perm (R U R' F' R U R' U' R' F R2 U' R') can replace the T-perm below.
Recognition
Headlights on all four sides of the top layer: solved (go straight to the edges). Headlights on exactly one side of the top layer: adjacent swap: turn the layer until they are on the left, then do a T-perm (R U R' U' R' F R2 U' R' U' R U R' F'). No headlights on the top layer: diagonal swap: do a Y-perm (F R U' R' U' R U R' F' R U R' U' R' F R F').
Source: Hand-written. Each case is SpeedCubeDB's published setup for a PLL with that corner swap but different edges (Ga for adjacent, V for diagonal), so no listed algorithm is the setup reversed; the algorithms are top-voted SpeedCubeDB PLL algorithms that make the swap, checked here for the corners alone. Every algorithm shown was checked by the logic engine; rejected ones are listed in docs/db-exclusions.md.