Roadhouse
It was SOP in the '50s and '50s to have a studio player do uncredited work .
Mack *is* credited on the album, but only as the bass player. I just checked two different books on the Doors, including Ray Manzarek's (the Doors keyboardist). Both of them list Mack as the bass player, and John Sebastian (from Lovin Spoonful) as the harp player (apparently a stage name for G. Puglese).