Boiling is just a term people use to get the tissue off of the skull. The correct term should be simmer, you should never let the water/detergent mixture get to a boil. Once the tissue is off of the skull I'll put about a 1/4 cup of Dawn dish washing detergent into the pot with enough water to cover the skull and simmer for a while longer and then rinse. Sometimes with very greasy skulls I'll do this twice or even three times.
The for the final prep I'll use some Basic White and the 40 volume crème developer and make a paste that I can brush on with a small 1" paint brush. Then place it in a plastic bag and let it sit for a few days. The final rinse is just plain old water.
Here is the whole process that I do with fresh skulls but the last part will work for one that is close to being ready to hang:
1. Don't fret about taking all the meat, brains, etc. out before hand. Get what you can.
2. If you don't mind some smell, it doesn't hurt to let the skull "ripen" a bit. I usually wrap in plastic bags and let them sit for a few days. Not necessary, but speeds up the process a bit.
3. NEVER BOIL, as in don't ever BOIL a skull.
4. Get some sal soda (washing soda). I usually put 1-2 cups in my (large) "boiling" (again don't boil a skull, EVER) pot. Simmer for a couple hours. The key here is the washing soda, the cartilage, meat, etc. will literally start falling off and you don't need to scrape, power wash, use brushes, none of that B.S.
5. Replace water, this time I usually put just a bit more sal soda (not much) and about a half bottle of dawn, and dawn dish soap only. Simmer, did I mention to NEVER BOIL???, for a few hours. For greasy skulls like bears, I usually repeat this step to make sure the grease is all pulled from the skull.
6. Go to a Sally's or some other beauty supply store that has hair salon stuff...pick up a gallon container of 40 volume crème developer, while you're there, get a container of basic white (powdered stuff). Trust me on the gallon size, you'll be doing this every time you do a skull from here on out.
7. Fill a plastic bowl with basic white and mix in the crème developer...it should be smooth, thickish paste. Be careful to NOT get any of this on antlers, unless you like white antlers. I use a paint brush and paint the mixture all over the skull, don't get cheap, apply it pretty heavy. Wrap the skull in plastic bags (I usually use plastic grocery store bags for deer and pronghorn, use tall white kitchen bags for elk). Walk away for 3-5 days.
8. Open bag, rinse the skull in water and let dry.