Suicide notes are written documents left behind by suicide victims, either on paper or on social media, and can help us understand the mentality and thought processes of those struggling with suicidal thoughts. In our preliminary work, we have proposed the use of Time Perspective (TP), which takes into consideration how people think of or appraise their past, present, or future life would shape their behavior, in suicide tendency detection based on suicide notes. The detection result is highly dependent upon a ternary classification task that groups any suicide tendency into one of the three pre-defined types. In this work, we define the suicidal emotion trajectory, a concept that is based on TP and used for depicting the dynamic evolution of an individual's emotional state over time, and this trajectory serve as an auxiliary task to the primary ternary classification task for a multi-task learning model, i.e. TP-MultiBert. The model features Bidirectional Encoder Representation from Transformer (BERT) components, replacing its counterpart, i.e., GloVe, in the previous model. Thanks to its desirable capability of understanding word contextual relationships, as well as multi-task learning capability of leveraging complementary information from various tasks, BERT shows promissing results in further improving the performance of suicide ideation detection.