I've got the very 1st edition SMC alky kit on my car. The pump has died 3 times now over 7-8 years, but it's because I always forget about it when winter comes and the alky/water eat it and lock it up. I always have to test it or change it before I take it out when Spring comes every year.
About that green light......yeah it should come on when you hit the test button. That means its working. But you really won't know for sure, because a locked up pump will still receive the signal and turn the light on, but not pump anything. What you need to do is steal your wife, or a kid, or a neighbors kid and put their rump in the drivers seat while you hold a hose in a bucket that is connected to your kit and watch it pump with your own eyes. Have them work the speed dial on the controller and make sure it slows down as it gets closer to zero and speeds up all the way to 10.
That's all I do every Spring and I never have any problems with mine.
When I have to replace the pump, it's an Airtex unit from older Chryslers that can be picked up from Rock Auto or Advance Auto Parts stores anywhere.