Adapting pre-trained deep learning models to new and unknown environments remains a major challenge in underwater acoustic localization. We show that although the performance of pre-trained models suffers from mismatch between the training and test data, they generally exhibit a higher uncertainty in environments where there is more mismatch. Additionally, in the presence of environmental mismatch, spurious peaks can appear in the output of classification-based localization approaches, which inspires us to define and use a method to quantify the "implied uncertainty" based on the number of model output peaks. Leveraging this notion of implied uncertainty, we partition the test samples into sets with more certain and less certain samples, and implement a method to adapt the model to new environments by using the certain samples to improve the labeling for uncertain samples, which helps to adapt the model. Thus, using this efficient method for model uncertainty quantification, we showcase an innovative approach to adapt a pre-trained model to unseen underwater environments at test time. This eliminates the need for labeled data from the target environment or the original training data. This adaptation is enhanced by integrating an independent estimate based on the received signal energy. We validate the approach extensively using real experimental data, as well as synthetic data consisting of model-generated signals with real ocean noise. The results demonstrate significant improvements in model prediction accuracy, underscoring the potential of the method to enhance underwater acoustic localization in diverse, noisy, and unknown environments.