I think the original poster said he has already replaced the battery and checked the ground. However, he didn't say if he had brushed it around the cable ring to remove paint to get a good ground.
I really don't think it is the SJB causing his problem but I guess we'll see.
Yes the SJB may be the issue as everything seems to go through it. While my light problem is "gone" for now, it would be good to know what the root cause may be. Nothing in my automotive experience can explain a light turning on when the car is parked and unattended. Sticky switch? Circuit jumping? Moisture/corrosion? A physical reason that is so far undiscovered and thus my hope is to find an explainable solution.