We recently demonstrated that drowsiness, indexed using EEG, was associated with left-inattention in a group of 26 healthy right-handers. This has been linked to alertness-related modulation of spatial bias in left neglect patients and the greater persistence of left, compared with right, neglect following injury. Despite handedness being among the most overt aspects of human lateralization, studies of this healthy analogue of left neglect have only been conducted with predominantly or exclusively right-handed individuals. Here, with a group of 26 healthy non-right-handers we demonstrate that, unlike right-handers who showed a rightward shift in attention with drowsiness, non-right-handers showed the opposite pattern on an auditory spatial localization task. The current results are the first indication that factors linked to handedness can affect the development and extremity of spatial biases, potentially conferring resilience to clinical symptoms in non-right-handers and, given that 90% of us are right-handed, why left neglect is disproportionately persistent.