A critical aspect of mobile just-in-time (JIT) health intervention is proper delivery timing, which correlates with successfully promoting target behaviors. Despite extensive prior studies on interruptibility, however, our understanding of the receptivity of mobile JIT health intervention is limited. This work extends prior interruptibility models to capture the JIT intervention process by including multiple stages of conscious and subconscious decisions. We built BeActive, a mobile intervention system for preventing prolonged sedentary behaviors, and we collected users' responses to a given JIT support and relevant contextual factors and cognitive/physical states for three weeks. Using a multi-stage model, we systematically analyzed the responses to deepen our understanding of receptivity using a mixed methodology. Herein, we identify the key factors relevant to each stage outcome and show that the receptivity of JIT intervention is nuanced and context-dependent. We propose several practical design implications for mobile JIT health intervention and context-aware computing.