On our '07 H180 the light does come on as well when the float switch triggers the pump.
We struggled all of last summer with bilge pump switch problems. The switch would stick in the on position just enough when triggered by rainwater or acumulation. But, if you tried to re-create a "sticking" situation(pouring water into the bilge), the switch would work just fine. Every couple of weeks after a good rain storm, we would arrive at the marina and jump onto the boat to find the pump running dry with the switch stuck in the on position again (yes luckily we didn't run the battery flat, mostly because I am anal about checking the boat out after any kind of stormy weather).
At the end of the season, I bought one of these guys to replace the faulty switch:
http://www.johnson-pump.com/JPMarine/products/bilge/ultimaswitch.htmlI will be installing it this week, so unfortunately I can't tell you anything more about it other than I think it is a great idea. I was planning on posting a few pics of my install once it is done, so if anyone is interested, keep your eyes on the forum for my post.