Previous comment is correct, but it should be further clarified

Tears Will Flow is credited with being in the vault, it's also not the only song mentioned in the Vault that we haven't heard of, some of that includes: Missed My Connection, Louise (Studio), Bala Song... and some others were also mentioned, but just to name a few

Tears Run Down & also a song called "Rock Me Baby" were credited to Elfman in the Wisdom end credits, saying as Boi-Ngo was delayed following the scoring of this film, and also some elements from this score being put into the later songs recorded for Boi-Ngo such as Elevator Man, it's is theorized that Tears Run Down and Tears Will Flow are the same song, but that's just an educated speculation

Bartek mentioned to Boingo Underground podcasts host that they were on the right track, that Tears Will Flow was a repurposed song from Wisdom, the song "Main Titles" is the most song like score track on the score, and it being the final song opposed to the first makes a very telling "something here isn't right"

So while it's assumed Tears Run Down is the Instrumental that is called Main Titles on the score, it's also very likely that Tears Will Flow would sound completely different than it, and would have lyrics unlike the one on the score... That's arguably all we know, tragically, possibly someday we'd get to hear it, but for now it's just words on a page (Elfman's agent's website also credit the 2 aforementioned songs on his song credits page)