Social media data is increasingly used to gain insights into trends in mental health, but prior studies aimed at confirming a link between online expression of suicidal ideation on social media and actual suicide deaths have been inconclusive. Using comprehensive six-year data sets of Twitter posts and suicide deaths in Japan, we examine the diurnal relationship between the proportional incidence of a suicide-related keyword, "kietai" ("I want to disappear"), and suicide deaths with an OLS regression model. We also use co-occurrence analysis to reveal changes in the linguistic context of the suicide-related keyword at different hours of the day. We find a clear diurnal pattern in the use of this suicide-related keyword, peaking between 1am and 5am. This diurnal trend is positively correlated with suicide deaths among younger cohorts (ages 15 to 44), but the correlation is negative among older adults (45 and over). The correlation among young adults strengthens when a delay between tweet incidence and suicide deaths is included. Compared to daytime tweets, nighttime tweets exhibited a stronger relationship between words related to self-disgust and words directly indicating suicidal intent. This study confirms the hypothesised link between online suicidal ideation and suicide death. Despite frequent flippant use of the keyword, the consistent correlation and the diurnal changes in the context of the keyword's usage demonstrate the value of social media data to the study of mental health trends in groups at risk of suicide.