Yep, quite happy I know what the Cruise Control does, been using in pretty much the way you describe for the last four and half years - thanks for asking though.
The OP says he noticed it when parking, not sure that means that it only came on when he was parking though, could have come on earlier in the journey. I'm sure he'll be along in a while to clarify.
Strange thing you mention about the dashboard light though, mine stays on as long as it's activated but not set whereas it would seem yours goes out once you hit the brake. Mine's a 56 model so maybe a change in later MYs?