The health outcomes of high-need patients can be substantially influenced by the degree of patient engagement in their own care. The role of care managers (CMs) includes enrolling patients and keeping them sufficiently engaged in care programs, so that patients complete assigned goals leading to improvement in their health outcomes. Here, we present a data-driven behavioral engagement scoring (BES) pipeline that can compute the patients' engagement level with regards to their interest in: (1) enrolling into a relevant care program, and (2) completing program goals. This score is leveraged to predict a patient's propensity to respond to CMs' actions. Using real-world care management data, we show that the BES pipeline successfully predicts patient engagement and provides interpretable insights to CMs, using prototypical patient cases as a point of reference, without sacrificing prediction performance.