Tamyrlin: 2002-11-11

The song is symbolic of the peace they had before the Breaking. They wandered after the Breaking looking for that peace again that Rand saw while in Rhuidean. The actually singing they did doesn't appear to be that "special". It doesn't do anything for them. They ask the question about the song because it is tradition, not because they are literally hoping to hear someone sing a specific song. Growing songs are common among Loial's people. Perrin will be instrumental in helping the Tinkers find that peace. But then again, I have always disagreed with the idea that the song was literal and always probably will...unless you have some quotes beyond the ones you have mentioned? :) I will see what I can do about convincing you otherwise soon when I defend my faction on the message board.

ArgotzGoldenEyes: 2013-01-21

I dont know if this help, but here it is.

"That's why they travel," Elyas said, "or so they say. They're looking for a song. That's what the Mahdi seeks. They say they lost it during the Breaking of the World, and if they can find it again, the paradise of the Age of Legends will return." He ran his eye around the camp and snorted. "They don't even know what the song is; they claim they'll know it when they find it. They don't know how it's supposed to bring paradise, either, but they've been looking near to three thousand years, ever since the Breaking. I expect they'll be looking until the Wheel stops turning."
-EoTW Chp.25

It is also known that the Traveling People, before the breaking of the world, were the Da'shain Aiel(mayhap mispelled) and were servants to the Aes Sedai. They had a knowledge and skill known as seedsining, which they worked with the Oiger, to sing and grow crops. This was lost during the Breaking of the World. Now, the Traveling People, search for this song, in hopes that when they re-learn it, they can bring peace, and paradise back to the World. Rand had seen this son, during his vision at Rhueidan, and spoke of it, and Perrin somehow lets the Traveling People know of it. This can also be read at wikipedia.com.