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TV on the Radio – Staring At The Sun Lyrics 19 years ago
Here's my guess on this song.
A lady was driving in front of a store and hit a sign, and now her lover is giving her mouth-to-mouth resuscitation and CPR.

Now, whether the wreck happened on an actual beach or not, I don't know... the author might be making a reference to the fact that since she's not breathing (in fact, suffocating), it's like drowning. I don't know...half the song is from the point of view of the victim, and part from her lover.

But here's a breakdown.
cross the street from your storefront cemetary: He approaches her body
hear me hailing from inside and realize I am the conscience clear in pain or ecstacy: he's calling her to "come back from the light," so to speak. And telling her he's trustworthy
we were all weaned my dear upon the same fatigue:
we all get tired of living once we grow up

staring at the sun: she's on her back as he gives CPR
standing in the sea: either it's a literal beach, and he's just above the surf, or the "water" is a suffocation death (since she's not breathing).
your mouth is open wide: that's cause she's unconscious, and it's the position you put someone in to give mouth-to-mouth
the lover is inside: the victim is his lover
and all the tumult's done: the car wreck is over (or, he just pulled her out of the surf, which is also a "tumult")
collided with the sign, you're standing in the sea: her feet are still being lapped by the water (literal or no)
the woman's part is the victim speaking: oh, my own voice cannot save me now (underwater, you can't talk), one more breath and then I go down (she's suffocating)

note the trees because the dirt is temporary: they're between the high tide line and the current level of the surf; trees don't grow below the high-tide line.

more to mine than fact, face, name and monetary: ambulances and stuff want your insurance info and vital stats, but he's saying that his lover ("mine") is more than just a bunch of facts.
be what you will and then throw down your life: either it's a suicide, or he's saying she's giving up the fight to stay alive
oh, it's a damned fine game, and we can play all night: sounds like he's saying if she does give up, he's going to keep giving CPR until she stops "playing around."

beat the skins: CPR
let the loose lips kiss you clean: mouth-to-mouth, and either it's a reference to the fact that you have to make sure the airway's unblocked (a "clean" airway) when you do mouth-to-mouth, or it's a reference to a non-sexual (i.e.: "clean") kiss
quietly pour out like light: leaving your body?
lightning in your teeth: not sure: a crash cart, and they're "shocking" her? or she has braces? or he has that metallic taste in his mouth from a lot of adrenaline (or drugs)? Not sure.

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