Domain adaptation (DA) techniques are frequently utilized to enhance seizure prediction accuracy by leveraging the labeled electroencephalogram data of existing patients on new patients. Traditional DA methods, however, require access to the source domain while training the adaptation model, which poses a threat to sensitive patient information and privacy. To address this issue, in this article, we propose a novel Gaussian mixture modeling (GMM)-based source-free domain adaptation (GSFDA). Our method leverages the GMM joint source model and target data structure for clustering, employs uncertainty learning to minimize DA uncertainty, and uses the mixup technique to increase model robustness while reducing the impact of noisy pseudolabels. Notably, GSFDA only requires access to the source model parameters, and not the source domain, effectively safeguarding the privacy of patient information. This has substantial clinical implications for seizure prediction.