Thanks for this njbray and pomero!
My car has, for years now, had the battery run down after a couple of weeks of sitting and it didn't matter how new the batteryt was. I always made a point to go start it or put it on the charger if I wasn't able to actually drive it for a while.
After changing my radio settings to turn off the LED then going away on a trip for three weeks, my car started right up when I returned! This would not have happened before.
Many, many thanks running this down (as it were) and letting us know what you found about the LED power usage. It is much appreciated!