Thinking Mode Fusion (TMF) enables large language models to support both concise responses and long-form reasoning by unifying a non-thinking mode and a thinking mode within a single model. However, its training dynamics, including the data ratio and training schedule between the two modes, remain underexplored. In this work, we present a systematic study of TMF by analyzing the effects of the training schedule and data ratio between thinking and non-thinking modes. Focusing on mathematical problem solving, we construct a benchmark with multiple thinking-to-non-thinking data ratios and three training schedules. Our results reveal an asymmetric interaction between the two modes: increasing the ratio of non-thinking supervision reduces the accuracy of the thinking mode. We further show that different training schedules modulate this trade-off and that the optimal schedule depends on the data ratio. Finally, we quantify a negative correlation between non-thinking and thinking mode supervision, highlighting an inherent tension between these two modes. These findings provide practical guidance for designing effective TMF training settings. All code and data are released to support further research at: Fusion Bench.