There's nothing wrong with the advice you're getting, regarding brumation. It does sound as though your snake has flipped the brumation switch ON, but it is not a foregone conclusion. Even if temperature is the stumulus for the fasting.
1. If your snake is not spending 80 % of it's daytime hours INSIDE the warm-side hide, it's body temperature is likely wrong. If the warm-side hide is too warm and/or not dark enough, snakes usually retreat to cage zones that may not be conducive to appetite and digestion. Regardless of the location of your thermometer, if your snake is not staying in that DIGESTING ZONE, all your efforts of heating are being wasted. If the temperature is correct in the primary hide in your cage, and if that hide offers another important utility (privacy and darkness), and if your snake is staying in that hide, but still refuses to eat, consider brumation. Of course, you only want to brumate if your snake is healthy. If stools are not normal, do not brumate. Atypical stools are a symptom of a problem that must be corrected quickly. If brumation is not adequate in terms of temperature, your snake's immune system can be compromised, and parasitic entities can gain the upper hand in the battle with your snake. Triple check temps INSIDE the primary hides before presuming your snake wants to brumate.
Re: lights over cages:
Corn snakes are essentially nocturnal. While they MAY benefit from light during the day, it does not necessarily follow that they like or NEED such lighting. Incandescent lights over cages (especially in winter) can contrubute to a decrease in ambient humidity (not a good thing), but among other overlooked dangers of those lights, retinal damage can result when the hide does not sufficiently protect your snake's eyes. In the absence of hands and eyelids to block UV radiation from their eyes, some snakes will not burrow into their cage's substrate where it's dark. Even if the warm-side hide in your cage is the correct temperature (only verifiable with a thermometer IN that hide), your snake may not utilize that hide if it does not offer the privacy they prefer. You have already observed that your snake is most active after dark. It's obvious they do not prefer brightly lit situations over dark ones. Hence, a primary hide must not only be the correct digesting appetite, but it must be dark enough to entice them to spend adequate time there.
SO, if you're certain it is 80F-85F INSIDE the hide, and if your snake spends most of the daytime hours in that hide, and if your snake's stools are normal, consider a cold, dormant period for your snake (15 days after its last meal). Otherwise, keep tweaking the cage conditions until you're certain you have provided the most primary digesting prerequisites. If you cannot offer a dark, cold (50F-65F) brumation, I recommend you keep working to make the cage more of a digesting environment for your snake.
Good luck,
Don
South Mountain Reptiles