Social media platforms are already engaged in leveraging existing online socio-technical systems to employ just-in-time interventions for suicide prevention to the public. These efforts primarily rely on self-reports of potential self-harm content that is reviewed by moderators. Most recently, platforms have employed automated models to identify self-harm content, but acknowledge that these automated models still struggle to understand the nuance of human language (e.g., sarcasm). By explicitly focusing on Twitter posts that could easily be misidentified by a model as expressing suicidal intent (i.e., they contain similar phrases such as ``wanting to die''), our work examines the temporal differences in historical expressions of general and emotional language prior to a clear expression of suicidal intent. Additionally, we analyze time-aware neural models that build on these language variants and factors in the historical, emotional spectrum of a user's tweeting activity. The strongest model achieves high (statistically significant) performance (macro F1=0.804, recall=0.813) to identify social media indicative of suicidal intent. Using three use cases of tweets with phrases common to suicidal intent, we qualitatively analyze and interpret how such models decided if suicidal intent was present and discuss how these analyses may be used to alleviate the burden on human moderators within the known constraints of how moderation is performed (e.g., no access to the user's timeline). Finally, we discuss the ethical implications of such data-driven models and inferences about suicidal intent from social media. Content warning: this article discusses self-harm and suicide.