Apparently the song is called "Flowers" performed by Ivri Lider and Tom Rahav. It appears in the 2004 film Walk on Water and was apparently made exclusively for the film. Anyways, here is the full-length version of my mix, transposed to the correct key and tweaked:
"Flowers Revisited"
"Mystery Song"
I was trying to find the name of this song, so I recreated the melody using a sequencer. I vaguely recall hearing this tune on TV. Does anybody here know it?