I believe suicidal tendencies is simply when the weight of feelings from depression, anxiety, and psychosis outweigh results from coping mechanisms. I don't think it has as much to do with feelings of sadness or lack of happiness.
Is happiness not a coping mechanism for anxiety?
That describes happiness as a method, rather than an effect or an outcome. But it's an effect, generally out of people's control except as a desirable outcome of things that really are methods, like jogging or crossword puzzles.
Happiness isn't a switch that you can throw, it's the light that results from throwing the switch.