The aquarium heater for de-greasing was a real game changer for me. This is all great and proven advise for skull cleanup.
In a perfect world I'd have a beetle colony in a controlled / clean environment., and then would degrease. I've simmered a few and just never been happy with the end result. Even at low temps, the bone develops a somewhat porous and textured surface. A) That surface accepts dust / dirt more easily that it would naturally. B) The simmered skulls I have, all have a grease spot here and there. My go to-method past few years is entire head (hide, eyes, tongue, brain) into a rot bucket. It stinks, but it leaves the bone so pretty. Then degrease.
I recommend hide, hair, tongue etc for two reason. One, it's a whole lot easier to not mess with removing them all. Two (and of equal importance), I have noticed that heads WITH hair actually clean themselves up quicker. I suspect that all of the surface area that each hair brings to game provides tons more bacteria to kick off the rotting process. A clean head into a clean bucket of water actually seems to take longer. For what that's worth.
For folks who aren't degreasing, I'd highly recommend this step. Even if you'd simmered the head. It goes such a long way in terms of a uniform color to the skull. By the degreasing step, you should be past the stinky part. So for those in cold environments, you can put bucket in a garage with aquarium heater. Insulating bucket might be necessary for some.
Oh, one thing I learned the hard way. I was rotting on head and I decided to put a trash bag over the system. This was a whitetail. Well, I take the bag off one day, and my antlers are pretty severely discolored. The bases and burs almost a translucent material, tips the same thing, and then even portions of beams and points had lost some color. I suspect that the bag essentially created a sauna. 100% humidity and a lot of heat trapped in there... ie: greenhouse. I wont' do that again. Definitely keep the antlers in open air during maceration and degreasing. Some potassium permanganate had the color in decent shape afterwards, but I still lost some accumulated debris from rubbing, plus other material on antler that keeps that more natural look with three dimensional colors.