Falling in love with Alex McMurray is easy. He possesses a certain unintentional charm, both onstage and off. It is the kind of charm specific to the perpetually heartbroken singer-songwriter who may or may not be on the brink of greatness. It is a cliché, this charm, but it is undeniable even as he bounces up and down, singing sea shanties, flanked by a washboard player and a sousaphone player, on Monday nights at El Matador.

It’s ...