What is known to be able to make two people out of one?

I shimmer where your longing leads, A promise born of burning needs. I paint you gifts you cannot claim, A distant pool without a name. You chase me, though I never stay, I live in heat, then fade away.

Shake me, change me, lend me, tie me. Near things are at me. If I feed you, don't bite me.

My first four are two, double take, see you. My last four are the four at the end of the last sixth of the twelve. Call in dear, we’re in a pickle.

I have a bark but cannot bite, I am very small and light, Broken off by the wind, you’ll see, I'm a tiny piece of a tree