The former Afghan Whig, who spearheaded grunge’s soulful tip, began these songs when his band split but shelved them in 2002 after the fatal heart attack of his friend, the film director Ted Demme. Made with several collaborators who later joined Dulli’s current combo, the Twilight Singers, Amber Headlights burns and throbs with Dulli’s signature wounded, ballsy style and his usual groin-related fixation (the opening So Tight begins: “It’s Friday, I’m lonely . . . girl, I’m set to pop”), but Demme’s ghost is all over the record, from an orchestrated Domani (“son of the morning star/vodka high, a little cocaine/you know who you are”) to the closing piano elegy Get the Wheel. Essential for fans and a good introduction for the curious.