One hypothesis some suicide researchers have floated is that suicide has multiple aspects; the dark winters damage people emotionally while reducing energy, and then when the light comes flooding back, their energy levels recover before their emotions. Result: suicide. Apparently there's some analogies in depression treatment where you're briefly more likely to commit suicide after a treatment starts working. Here's one paper on the topic: Vyssoki et al 2014 http://www.gwern.net/docs/2014-vyssoki.pdf "Direct Effect of Sunshine on Suicide". There might be something similar at play in Greenland.
That's interesting, and almost seem related to what you see in the first weeks of anti-depressant therapy (especially in teens). The depression and distorted thinking haven't changed, but they get a huge blast of energy. It's one of the possible explanations for why the first few weeks on an anti-depressant are particularly risky in terms of suicide.
It does take that odd combination of pain and energy to drive people to end their lives, not just despair and enervation.