This is a nice one! Music is by Ghulam Haider.
P.S. The tune reminds me a lot of something else, but I just can’t place it right now…
P.P.S. 1945 and 1946 were golden years for Rehana. I started looking at dances with her from these years after a blog conversation at Vidur’s “Bollywood Fun” blog about her appearance in Zeenat (1945), and the next day, I saw that Nivedita was starting to post some songs from Hum Ek Hain (1946), the film in which Rehana got her first major role. Sometime soon, I will probably do a post on some songs found at the end of her film career, in the early ’60s (which I like almost as much!).
Dances on the Footpath 
Lovely number, it reminds me of ‘mere piya ghar’ and this number below
Thanks for the fun suggestions, Bollywooddeewana. I don’t hear the similarity to “Mere Piyar Ghar” that much but I definitely heard pieces of the same song in “Ye Aahken Juhki Juhki Si,” and I’m glad to have the clip here too.
I don’t think this is the mysterious song that was nagging at me, and I might never figure out what that was But it’s good to hear about other songs that fit the bill. :)