Taking the data from both surveys, where Seattle was #2 in attempts from 2008-10, but behind Dallas and tied with Salt Lake City (both cities have more sunny days) and not even in the Top 10 of the other list (which appears to take data from the 90s-00s) and where several of the top places do get a lot of sunshine, the only logical deduction is that with this data there just doesn't appear to be any correlation between lack of sun and suicides.
Here's a WebMD article on Seasonal Affective Disorder (i.e. lack of sunlight in the winter). They mostly talk about Alaska and the Arctic region, where winter days are even shorter than in the PNW. Doesn't make any connection to suicide....doesn't even mention the word that I saw.