I would keep the basking light on for how ever long he seems to need it or you need it to maintain the correct ambient temperature. During winter I end up leaving my basking lights on all day, but that is because I am not able to heat my house.
Jackson's don't have a natural brumation because they don't have a sustained cold or dry season. In Kenya they have two wet and two dry seasons which don't have a whole lot of temperature variation between the two. That said, they are reptiles and they will respond to lower temperatures by being...