Hi Gayle, welcome to the forum.
Here in the UK, I only have a basic spec model with no active alarm system, but I assume someone with a higher trim model who do have an alarm system, will be able to help you. I personally never liked noisy alarm systems as no-one looks anymore, and will just walk on. Do not blame them either.
Is this the light that comes on? (taken from the manual)....
If so it says in the manual, that it should flash on and off continiously when alarm is activated when out of the car.
I would expect it to be off, if the alarm is off.
Not sure if Ecosport has the following....Some cars do have a method of telling you if the alarm went off while you were away from the car, for example interior movement sensor operation might be code 4, so the alarm light would flash on four times fast then off for a while, then four times fast again, etc, but should reset the next time car alarm is used.