Hi @Ivie54, welcome to the forum, and thanks for posting.
I've had a look at the BT3570 Product Help Page and the user guide (page19). I don't think the base light can be stopped but if your referring to the green light when there are messages I would expect it to stop once all messages were listened to.
Have a look at the link above, and the contact number for the Product Help Desk is listed so you can always give them a quick call to clarify.
The light confirms that the handset is charging or if another handset is on a call. If you want it gone you could always put a piece of electrical tape over it.