Foundation models have recently extended beyond natural language and vision to timeseries domains, including physiological signals. However, progress in electrodermal activity (EDA) modeling is hindered by the absence of large-scale, curated, and openly accessible datasets. EDA reflects sympathetic nervous system activity and is widely used to infer cognitive load, stress, and engagement. Yet very few wearable devices provide continuous, unobtrusive sensing, and the only large-scale archive to date is proprietary. To address this gap, we compile EDAMAME, a collection of EDA traces from 24 public datasets, comprising more than 25,000 hours from 634 users. Using this resource, we train UME, the first dedicated foundation model for EDA. In eight out of ten scenarios, UME outperforms baselines and matches generalist timeseries foundation models while using 20x fewer computational resources. Our findings, however, also highlight the intrinsic challenges of EDA modeling, motivating further research to unlock its full potential. All datasets, model weights, and code are released to support further research.