All of the fuel injectors have positive power when your key is in the run position. The pcm switches the negative to provide the injector pulse. I've attached a link that shows how a 1999 vortec 5.7's injectors are wired. I believe the LS1 would be similar except for the pin numbers. If you used connector #33, that would be a negative injector wire.
http://www.lt1swap.com/1999_vortec_5...20Controls.gif
I'm just about ready to turn the key on my 5.3 LM7 swap in an 83 Camaro and LT1swap.com has a ton of helpful info on wiring.
Hope this helps.