OK I just checked my pixel one so I could tell you what heappens with the lights. When I plug it in the lights flash for a second or two then go off. When I fire the flash one red light stays on and the red one on the right flashes for a few a moment until the it is ready to fire again. Then they are both on.
But if I dont fire it for a few seconds they both go off again and don't come back on until I fire it again.
So it seems the left one shows the flash has fired, the right one shows the status (ready to fire) by flashing while the capacitor is charged. But just having it plugged in they should both be off until you fire it.
And top the person who asked about a swith, no switch, just the 2 indicator lights.
BTW I am using it with an SB900, like I said I got mine from deal extreme, they are in China and do free shipping, it was 50 AUD which is just under a 1/3 the price I paid for my Nikon equivilents. But it did take me a long time to recieve it. I also dont like the pouch it came with as much as the Nikon one which has velcro so the belt clip thing on the back can open up and you can attach it easily to a light stand or whatever.
If you want a really nice pack look at the quantum ones, they make some great stuff, its expensive though (800 USD) but I also use a quantum flash off camera so needed one anyway. I got the optional camera cable with the turbo 3 pack, that will power my D3 in a pinch. This bad boy will power 2 speed lights, or a speed light and camera at the same time and has a built in fuel gauge. The have smaller packs like the SC and they are really good too.