Behaviour biometrics are being explored as a viable alternative to overcome the limitations of traditional authentication methods such as passwords and static biometrics. Also, they are being considered as a viable authentication method for IoT devices such as smart headsets with AR/VR capabilities, wearables, and erables, that do not have a large form factor or the ability to seamlessly interact with the user. Recent behavioural biometric solutions use deep learning models that require large amounts of annotated training data. Collecting such volumes of behaviour biometrics data raises privacy and usability concerns. To this end, we propose using SimSiam-based non-contrastive self-supervised learning to improve the label efficiency of behavioural biometric systems. The key idea is to use large volumes of unlabelled (and anonymised) data to build good feature extractors that can be subsequently used in supervised settings. Using two EEG datasets, we show that at lower amounts of labelled data, non-contrastive learning performs 4%-11% more than conventional methods such as supervised learning and data augmentation. We also show that, in general, self-supervised learning methods perform better than other baselines. Finally, through careful experimentation, we show various modifications that can be incorporated into the non-contrastive learning process to archive high performance.