A Rainbow in Curved Air by Terry Reilly?
I don’t have a clip handy, but when Apollo Creed hosted SNL many years ago, he sang a few lines of some song mentioning a rainbos.
Carl Weathers, about 2 minute into this clip from 01-30-1988, Watch Saturday Night Live Clip: Carl Weathers Monologue - NBC.com
But warning, his singing is terrible. The song is named “What About a Rainbow”
Oh, come on! How could you not mention “Double Rainbow”? It was literally the first one I could think of.
Rolling Stones - She’s A Rainbow.
After the wizard falls from his tower, his dismayed followers, suddenly without a purpose, see a rainbow on the horizon.
Look at my flesh and bone
Now, look, look, look, look
Look at his tower of stone
I see a rainbow rising
Look there, on the horizon
And I’m coming home, coming home, coming home
Look To the Rainbow from the musical/movie, “Finian’s Rainbow”.
Look, look, look to the rainbow;
Follow it over the hill and stream.
Look, look, look to the rainbow;
Follow the fellow who follows a dream.
Yes. As mentioned in the OP.
Gonna Find A Rainbow - The Brady Bunch kids (please don’t ban me!)