Graphical user interfaces (GUIs) are central interaction points in modern software systems, making GUI-based test automation a central and economically relevant part of software development by enabling the automated execution and assessment of user-visible interactions. Over time, it has evolved into a diverse and fragmented landscape, ranging from manual and deterministic approaches to increasingly autonomous, AI-supported solutions. While this diversity enables flexible testing strategies, it also confronts practitioners with a growing number of implicit design decisions that are rarely made explicit or systematically compared. This paper addresses this challenge by conceptualizing GUI-based test automation frameworks as a design space and proposing a design-oriented taxonomy to structure it. Following design science research, we developed the taxonomy based on an analysis of 103 GUI-based test automation frameworks. We complement the taxonomy with a cluster analysis to identify recurring combinations of design decisions across existing test automation frameworks. To demonstrate practical relevance and evaluate the taxonomy, we applied it to established, widely used test automation frameworks from practice. This evaluation illustrates how the taxonomy supports systematic comparison and informed reasoning about alternative design choices and trade-offs, such as human control versus autonomy. Overall, the paper contributes design knowledge that helps practitioners and researchers reason about GUI-based test automation beyond tool-centric perspectives.