"Rained on, Rained on"... is Brian
"it rained on de'mountain, de'mountain of love" is probably David Sandler
It was produced by Brian, Stephen Desper & David Sandler. I guess Brian delivered a rough basic instrumental track with Moog & Piano, Sandler & Desper added additional instruments & sound effects.
Why didn't he keep it for the Beach Boys!
Well, this is a rewrite of "My Solution".