Ok, went through did some checking on the start/stop function. It definitely didn't cut and restart the engine at traffic lights.
First thing I decided was that the battery was probably low, the car having been sitting in a lot for quite a while before we bought it. So, hooked up a trickle charger for a couple of days, and the light on it finally changed from solid red to solid green. All charged up now.
Then I took the car out for a drive,and now the start/stop function works as it should. This indicates to me that it can indeed act as "a canary in the coal mine" as you say, telling me that the battery is low.
The has always been running just as it should, with no warnings.