Other Tallguy, the song is from a Steve McQueen movie by the same title. Bernstein wrote the underscore, but I don't know if he wrote the song. I don't think he wrote the song, but others will know.
IMDb credits the title song to Elmer Bernstein (music) and Ernie Sheldon (lyrics) with the in-movie performance by Steve McQueen dubbed by Billy Strange! I came across this only a week or two ago whilst updating/correcting meta-tags of my music collection. A lovely song ... though I don't know the Glenn Yarbrough title song recording. On the soundtrack, the vocal is by The We Three Trio ... which may be the only tautologous group name in history! .
I always choose a tune that makes extensive use of piano, or even a solo piano cue. "Neverland: Piano Variation In Blue" from Finding Neverland (2004) in particular always works for me on days like that.
You're absolutely right - solo piano music of a certain kind is always reminiscent of rain. Sakamoto and Armstrong have produced albums full of it.